Introductory Statistics

Barbara Illowsky, Susan Dean

Chapter 2

Descriptive Statistics - all with Video Answers

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Chapter Questions

Problem 1

For each of the following data sets, create a stem plot and identify any outliers.
The miles per gallon rating for 30 cars are shown below (lowest to highest).
19, 19, 19, 20, 21, 21, 25, 25, 25, 26, 26, 28, 29, 31, 31, 32, 32, 33, 34, 35, 36, 37, 37, 38, 38, 38, 38, 41, 43, 43

Sandile Ndlovu

Sandile Ndlovu

Numerade Educator

Problem 2

For each of the following data sets, create a stem plot and identify any outliers.
The height in feet of 25 trees is shown below (lowest to highest).
25, 27, 33, 34, 34, 34, 35, 37, 37, 38, 39, 39, 39, 40, 41, 45, 46, 47, 49, 50, 50, 53, 53, 54, 54

Sandile Ndlovu

Numerade Educator

Problem 3

For each of the following data sets, create a stem plot and identify any outliers.
The data are the prices of different laptops at an electronics store. Round each value to the nearest ten.
249, 249, 260, 265, 265, 280, 299, 299, 309, 319, 325, 326, 350, 350, 350, 365, 369, 389, 409, 459, 489, 559, 569, 570, 610

Sandile Ndlovu

Numerade Educator

Problem 4

For each of the following data sets, create a stem plot and identify any outliers.
The data are daily high temperatures in a town for one month.
61, 61, 62, 64, 66, 67, 67, 67, 68, 69, 70, 70, 70, 71, 71, 72, 74, 74, 74, 75, 75, 75, 76, 76, 77, 78, 78, 79, 79, 95

Sandile Ndlovu

Numerade Educator

Problem 5

For the next three exercises, use the data to construct a line graph.
In a survey, 40 people were asked how many times they visited a store before making a major purchase. The results are shown in Table 2.37.
$$\begin{array}{|l|l|}\hline \text { Number of times in store } & {\text { Frequency }} \\ \hline 1 & {4} \\ \hline\end{array}$$
$$\begin{array}{|l|l|}\hline \text { Number of times in store } & {\text { Frequency }} \\ \hline 2 & {10} \\ \hline 3 & {16} \\ \hline 4 & {6} \\ \hline 5 & {4} \\ \hline\end{array}$$

Sandile Ndlovu

Numerade Educator

Problem 6

In a survey, several people were asked how many years it has been since they purchased a mattress. The results are shown in Table 2.38.
$$\begin{array}{|l|l|}\hline \text { Years since last purchase } & {\text { Frequency }} \\ \hline 0 & {2} \\ \hline 1 & {8} \\ \hline 2 & {13} \\ \hline 2 & {22} \\ \hline 4 & {16} \\ \hline 5 & {9} \\ \hline\end{array}$$

Sandile Ndlovu

Numerade Educator

Problem 7

Several children were asked how many TV shows they watch each day. The results of the survey are shown in Table 2.39.
$$
\begin{array}{|l|l|}\hline \text { Number of TV Shows } & {\text { Frequency }} \\ \hline 0 & {12} \\ \hline 1 & {18} \\ \hline 2 & {36} \\ \hline 3 & {7} \\ \hline 4 & {2} \\ \hline\end{array}
$$

Sandile Ndlovu

Numerade Educator

Problem 8

The students in Ms. Ramirez’s math class have birthdays in each of the four seasons. Table 2.40 shows the four seasons, the number of students who have birthdays in each season, and the percentage (%) of students in each group. Construct a bar graph showing the number of students.
$$
\begin{array}{|l|l|}\hline \text { Seasons } & {\text { Number of students }} & {\text { Proportion of population }} \\ \hline \text { Spring } & {8} & {24 \%} \\ \hline \text { Summer } & {9} & {26 \%} \\ \hline \text { Autumn } & {11} & {32 \%} \\ \hline \text { Winter } & {6} & {18 \%} \\ \hline\end{array}
$$

Rebecca Belvin

Numerade Educator

Problem 9

Using the data from Mrs. Ramirez’s math class supplied in Exercise 2.8, construct a bar graph showing the percentages.

Sandile Ndlovu

Numerade Educator

Problem 10

David County has six high schools. Each school sent students to participate in a county-wide science competition. Table 2.41 shows the percentage breakdown of competitors from each school, and the percentage of the entire student population of the county that goes to each school. Construct a bar graph that shows the population percentage of competitors from each school.

(TABLE CAN'T COPY)

Sandile Ndlovu

Numerade Educator

Problem 11

Use the data from the David County science competition supplied in Exercise 2.10. Construct a bar graph that shows the county-wide population percentage of students at each school.

Sandile Ndlovu

Numerade Educator

Problem 12

Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars. Complete the table.
(TABLE CAN'T COPY)

Sandile Ndlovu

Numerade Educator

Problem 13

What does the frequency column in Table 2.42 sum to? Why?

Sandile Ndlovu

Numerade Educator

Problem 14

What does the relative frequency column in Table 2.42 sum to? Why?

Sandile Ndlovu

Numerade Educator

Problem 15

What is the difference between relative frequency and frequency for each data value in Table 2.42?

Sandile Ndlovu

Numerade Educator

Problem 16

What is the difference between cumulative relative frequency and relative frequency for each data value?

Sandile Ndlovu

Numerade Educator

Problem 17

To construct the histogram for the data in Table 2.42, determine appropriate minimum and maximum x and y values and the scaling. Sketch the histogram. Label the horizontal and vertical axes with words. Include numerical scaling.

Sandile Ndlovu

Numerade Educator

Problem 18

Construct a frequency polygon for the following:

$$ a.\begin{array}{|c|c|}\hline \text { Pulse Rates for Women } & {\text { Frequency }} \\ \hline 60-69 & {12} \\ \hline 70-79 & {14} \\ \hline 80-79 & {11} \\ \hline 90-99 & {1} \\ \hline 100-109 & {1} \\ \hline 100-119 & {1} \\ \hline 120-129 & {1} \\ \hline\end{array}$$
$$b.\begin{array}{|c|c|}\hline \text { Actual Speed in a 30 MPH zone } & {\text { Frequency }} \\ \hline 42-45 & {25} \\ \hline 46-49 & {14} \\ \hline 46-49 & {14} \\ \hline 50-53 & {7} \\ \hline 54-57 & {3} \\ \hline 58-61 & {1} \\ \hline\end{array}$$
$$c.\begin{array}{|c|c|}\hline \text { Tar (mg) in Nonfiltered cigarettes } & {\text { Frequency }} \\ \hline 10-13 & {1} \\ \hline 14-17 & {0} \\ \hline 14-21 & {15} \\ \hline 22-25 & {7} \\ \hline 26-29 & {7} \\ \hline\end{array}$$

Sandile Ndlovu

Numerade Educator

Problem 19

Construct a frequency polygon from the frequency distribution for the 50 highest ranked countries for depth of hunger.
$$
\begin{array}{|c|c|}\hline \text { Depth of Hunger } & {\text { Frequency }} \\ \hline 230-259 & {21} \\ \hline 260-289 & {13} \\ \hline 260-389 & {5} \\ \hline 390-349 & {7} \\ \hline 320-349 & {1} \\ \hline 380-409 & {1} \\ \hline 410-439 & {1} \\ \hline\end{array}
$$

Sandile Ndlovu

Numerade Educator

Problem 20

Use the two frequency tables to compare the life expectancy of men and women from 20 randomly selected countries. Include an overlayed frequency polygon and discuss the shapes of the distributions, the center, the spread, and any outliers. What can we conclude about the life expectancy of women compared to men?
$$\begin{array}{|c|c|}\hline \text { Life Expectancy at Birth - women } & {\text { Frequency }} \\ \hline 49-55 & {3} \\ \hline 56-62 & {3} \\ \hline 63-62 & {1} \\ \hline 70-76 & {3} \\ \hline 77-83 & {8} \\ \hline 84-90 & {2} \\ \hline\end{array}$$
Table 2.47
$$\begin{array}{|c|c|}\hline \text { Life Expectancy at Birth - Men } & {\text { Frequency }} \\ \hline 49-55 & {3} \\ \hline 56-62 & {3} \\ \hline 63-62 & {1} \\ \hline 70-6 & {1} \\ \hline 77-83 & {7} \\ \hline 84-90 & {5} \\ \hline\end{array}$$
Table 2.48

Ahmad Reda

Numerade Educator

Problem 21

Construct a times series graph for (a) the number of male births, (b) the number of female births, and (c) the total number of births.

$$\begin{array}{|l|l|l|l|l|l|}\hline \text { Sex/Year } & {1855} & {1856} & {1857} & {1858}& {1859} & {1860} & {1861} \\ \hline \text { Female } & {45,545} & {49,582} & {50,257} & {50,324}& {51,915} & {51,220} & {52,403} \\ \hline \text { Male } & {47,804} & {52,239} & {53,158} & {53,694}& {54,628} & {54,409} & {54,606} \\ \hline \text { Total } & {93,349} & {101,821} & {103,415} & {104,018}& {106,543} & {105,629} & {107,009}\\ \hline\end{array}$$
Table 2.49

$$\begin{array}{|l|l|l|l|l|l|}\hline \text { Sex/Year } & {1862} & {1863} & {1864} & {1865}& {1866} & {1867} & {1868}& {1869} \\ \hline \text { Female } & {51,812} & {53,115} & {54,959} & {54,850}& {55,307} & {55,527} & {56,292}& {55,033} \\ \hline \text { Male } & {55,257} & {56,226} & {57,374} & {58,220}& {58,360} & {58,517} & {59,222}& {58,321} \\ \hline \text { Total } & {107,069} & {109,341} & {112,333} & {113,070}& {113,667} & {114,044} & {115,514} & {113,354}\\ \hline\end{array}$$
Table 2.50

$$\begin{array}{|l|l|l|l|l|l|}\hline \text { Sex/Year } & {1871} & {1870} & {1872} & {1871}& {1872} & {1827} & {1874}& {1875} \\ \hline \text { Female } & {56,099} & {56,431} & {57,472} & {56,099}& {57,472} & {58,233} & {60,109}& {60,146} \\ \hline \text { Male } & {60,029} & {58,959} & {61,293} & {60,029}& {61,293} & {61,467} & {63,602}& {63,432} \\ \hline \text { Total } & {116,128} & {115,390} & {118,765} & {116,128}& {118,765} & {119,700} & {123,711} & {123,578}\\ \hline\end{array}$$
Table 2.51

Sandile Ndlovu

Numerade Educator

Problem 22

The following data sets list full time police per 100,000 citizens along with homicides per 100,000 citizens for the city of Detroit, Michigan during the period from 1961 to 1973.

$$\begin{array}{|l|l|l|l|l|l|l|l|}\hline \text { Year } & {1961} & {1962} & {1963} & {1964} & {1965} & {1966} & {1967} \\ \hline \text { Police } & {260.35} & {269.8} & {272.04} & {272.96} & {272.51} & {261.34} & {268.89} \\ \hline \text { Homicides } & {8.6} & {8.9} & {8.52} & {8.89} & {13.07} & {14.57} & {21.36} \\ \hline\end{array}$$
Table 2.52
$$\begin{array}{|l|l|l|l|l|l|l|}\hline \text { Year } & {1968} & {1969} & {1970} & {1971} & {1972} & {1973} \\ \hline \text { Police } & {295.99} & {319.87} & {341.43} & {356.59} & {376.69} & {390.19} \\ \hline \text { Homicides } & {28.03} & {31.49} & {37.39} & {46.26} & {47.24} & {52.33} \\ \hline\end{array}$$
Table 2.53
a. Construct a double time series graph using a common $x$ -axis for both sets of data.
b. Which variable increased the fastest? Explain.
c. Did Detroit's increase in police officers have an impact on the murder rate? Explain.

Dani Dutmer

Numerade Educator

Problem 23

Listed are 29 ages for Academy Award winning best actors in order from smallest to largest.
18; 21; 22; 25; 26; 27; 29; 30; 31; 33; 36; 37; 41; 42; 47; 52; 55; 57; 58; 62; 64; 67; 69; 71; 72; 73; 74; 76; 77
a. Find the $40^{\text { th }}$ percentile.
b. Find the $78^{\text { th }}$ percentile.

Prabhakar Kumar

Prabhakar Kumar

Numerade Educator

Problem 24

Listed are 32 ages for Academy Award winning best actors in order from smallest to largest.
18; 18; 21; 22; 25; 26; 27; 29; 30; 31; 31; 33; 36; 37; 37; 41; 42; 47; 52; 55; 57; 58; 62; 64; 67; 69; 71; 72; 73; 74; 76; 77
a. Find the percentile of 37.
b. Find the percentile of 72.

Linh Vu

Numerade Educator

Problem 25

Jesse was ranked 37th in his graduating class of 180 students. At what percentile is Jesse’s ranking?

Rabia Shuaib

Numerade Educator

Problem 26

a. For runners in a race, a low time means a faster run. The winners in a race have the shortest running times. Is it more desirable to have a finish time with a high or a low percentile when running a race?
b. The 20th percentile of run times in a particular race is 5.2 minutes. Write a sentence interpreting the 20th percentile in the context of the situation.
c. A bicyclist in the 90th percentile of a bicycle race completed the race in 1 hour and 12 minutes. Is he among the fastest or slowest cyclists in the race? Write a sentence interpreting the 90th percentile in the context of the situation.

Christina Manahan

Christina Manahan

Numerade Educator

Problem 27

a. For runners in a race, a higher speed means a faster run. Is it more desirable to have a speed with a high or a low percentile when running a race?
b. The 40th percentile of speeds in a particular race is 7.5 miles per hour. Write a sentence interpreting the 40th percentile in the context of the situation.

Linh Vu

Numerade Educator

Problem 28

On an exam, would it be more desirable to earn a grade with a high or low percentile? Explain.

Marc Lauzon

Numerade Educator

Problem 29

Mina is waiting in line at the Department of Motor Vehicles (DMV). Her wait time of 32 minutes is the 85th percentile of wait times. Is that good or bad? Write a sentence interpreting the 85th percentile in the context of this situation.

Marc Lauzon

Numerade Educator

Problem 30

In a survey collecting data about the salaries earned by recent college graduates, Li found that her salary was in the 78th percentile. Should Li be pleased or upset by this result? Explain.

Linh Vu

Numerade Educator

Problem 31

In a study collecting data about the repair costs of damage to automobiles in a certain type of crash tests, a certain model of car had $1,700 in damage and was in the 90th percentile. Should the manufacturer and the consumer be pleased or upset by this result? Explain and write a sentence that interprets the 90th percentile in the context of this problem.

Linh Vu

Numerade Educator

Problem 32

The University of California has two criteria used to set admission standards for freshman to be admitted to a college in the UC system:
a. Students' GPAs and scores on standardized tests (SATs and ACTs) are entered into a formula that calculates an "admissions index" score. The admissions index score is used to set eligibility standards intended to meet the goal of admitting the top 12% of high school students in the state. In this context, what percentile does the top 12% represent?
b. Students whose GPAs are at or above the 96th percentile of all students at their high school are eligible (called eligible in the local context), even if they are not in the top 12% of all students in the state. What percentage of students from each high school are "eligible in the local context"?

Joshua Argo

Numerade Educator

Problem 33

Suppose that you are buying a house. You and your realtor have determined that the most expensive house you can afford is the 34th percentile. The 34th percentile of housing prices is $240,000 in the town you want to move to. In this town, can you afford 34% of the houses or 66% of the houses?

Marc Lauzon

Numerade Educator

Problem 34

Use Exercise 2.25 to calculate the following values:
First quartile $=$ ____

Linh Vu

Numerade Educator

Problem 35

Use Exercise 2.25 to calculate the following values:
Second quartile $=$ median $=50^{\text { th }}$ percentile $=$ ____

Harsh Gadhiya

Numerade Educator

Problem 36

Use Exercise 2.25 to calculate the following values:
Third quartile $=$ ____

Linh Vu

Numerade Educator

Problem 37

Use Exercise 2.25 to calculate the following values:
Interquartile range $(I Q R)=$ ____ - ____ $=$ ____

Harsh Gadhiya

Numerade Educator

Problem 38

Use Exercise 2.25 to calculate the following values:
$10^{\text { th }}$ percentile $=$ _____

Linh Vu

Numerade Educator

Problem 39

$70^{\text {th }}$ percentile $=$

Linh Vu

Numerade Educator

Problem 40

Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars.
Construct a box plot below. Use a ruler to measure and scale accurately.

Sandile Ndlovu

Numerade Educator

Problem 41

Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars.
Looking at your box plot, does it appear that the data are concentrated together, spread out evenly, or concentrated in some areas, but not in others? How can you tell?

Sandile Ndlovu

Numerade Educator

Problem 42

Find the mean for the following frequency tables.
a. (TABLE CAN'T COPY)
b. (TABLE CAN'T COPY)
c. (TABLE CAN'T COPY)

Sandile Ndlovu

Numerade Educator

Problem 43

Use the following information to answer the next three exercises: The following data show the lengths of boats moored in a marina. The data are ordered from smallest to largest: 16; 17; 19; 20; 20; 21; 23; 24; 25; 25; 25; 26; 26; 27; 27; 27; 28; 29; 30; 32; 33; 33; 34; 35; 37; 39; 40
Calculate the mean.

Sandile Ndlovu

Numerade Educator

Problem 44

Use the following information to answer the next three exercises: The following data show the lengths of boats moored in a marina. The data are ordered from smallest to largest: 16; 17; 19; 20; 20; 21; 23; 24; 25; 25; 25; 26; 26; 27; 27; 27; 28; 29; 30; 32; 33; 33; 34; 35; 37; 39; 40
Identify the median.

Sandile Ndlovu

Numerade Educator

Problem 45

Use the following information to answer the next three exercises: The following data show the lengths of boats moored in a marina. The data are ordered from smallest to largest: 16; 17; 19; 20; 20; 21; 23; 24; 25; 25; 25; 26; 26; 27; 27; 27; 28; 29; 30; 32; 33; 33; 34; 35; 37; 39; 40
Identify the mode.

Sandile Ndlovu

Numerade Educator

Problem 46

Use the following information to answer the next three exercises: Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars. Calculate the following:
sample mean $=\overline{x}=$____

Sandile Ndlovu

Numerade Educator

Problem 47

Use the following information to answer the next three exercises: Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars. Calculate the following:
median $=$____

Sandile Ndlovu

Numerade Educator

Problem 48

Use the following information to answer the next three exercises: Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars. Calculate the following:
mode $=$____

Sandile Ndlovu

Numerade Educator

Problem 49

Use the following information to answer the next three exercises: State whether the data are symmetrical, skewed to the left, or skewed to the right.
1; 1; 1; 2; 2; 2; 2; 3; 3; 3; 3; 3; 3; 3; 3; 4; 4; 4; 5; 5

Sandile Ndlovu

Numerade Educator

Problem 50

Use the following information to answer the next three exercises: State whether the data are symmetrical, skewed to the left, or skewed to the right.
16; 17; 19; 22; 22; 22; 22; 22; 23

Sandile Ndlovu

Numerade Educator

Problem 51

Use the following information to answer the next three exercises: State whether the data are symmetrical, skewed to the left, or skewed to the right.
87; 87; 87; 87; 87; 88; 89; 89; 90; 91

Sandile Ndlovu

Numerade Educator

Problem 52

Use the following information to answer the next three exercises: State whether the data are symmetrical, skewed to the left, or skewed to the right.
When the data are skewed left, what is the typical relationship between the mean and median?

Sandile Ndlovu

Numerade Educator

Problem 53

Use the following information to answer the next three exercises: State whether the data are symmetrical, skewed to the left, or skewed to the right.
When the data are symmetrical, what is the typical relationship between the mean and median?

Sandile Ndlovu

Numerade Educator

Problem 54

Use the following information to answer the next three exercises: State whether the data are symmetrical, skewed to the left, or skewed to the right.
What word describes a distribution that has two modes?

Sandile Ndlovu

Numerade Educator

Problem 55

Use the following information to answer the next three exercises: State whether the data are symmetrical, skewed to the left, or skewed to the right.
Describe the shape of this distribution.

Sandile Ndlovu

Numerade Educator

Problem 56

Describe the relationship between the mode and the median of this distribution.
(GRAPH CAN'T COPY)

Sandile Ndlovu

Numerade Educator

Problem 57

Describe the relationship between the mean and the median of this distribution.
(GRAPH CAN'T COPY)

Sandile Ndlovu

Numerade Educator

Problem 58

Describe the shape of this distribution.
(GRAPH CAN'T COPY)

Sandile Ndlovu

Numerade Educator

Problem 59

Describe the relationship between the mode and the median of this distribution.
(GRAPH CAN'T COPY)

Sandile Ndlovu

Numerade Educator

Problem 60

Are the mean and the median the exact same in this distribution? Why or why not?
(GRAPH CAN'T COPY)

Sandile Ndlovu

Numerade Educator

Problem 61

Describe the shape of this distribution.
(GRAPH CAN'T COPY)

Sandile Ndlovu

Numerade Educator

Problem 62

Describe the relationship between the mode and the median of this distribution.
(GRAPH CAN'T COPY)

Sandile Ndlovu

Numerade Educator

Problem 63

Describe the relationship between the mean and the median of this distribution.
(GRAPH CAN'T COPY)

Sandile Ndlovu

Numerade Educator

Problem 64

The mean and median for the data are the same.
3; 4; 5; 5; 6; 6; 6; 6; 7; 7; 7; 7; 7; 7; 7
Is the data perfectly symmetrical? Why or why not?

Sandile Ndlovu

Numerade Educator

Problem 65

Which is the greatest, the mean, the mode, or the median of the data set?
11; 11; 12; 12; 12; 12; 13; 15; 17; 22; 22; 22

Sandile Ndlovu

Numerade Educator

Problem 66

Which is the least, the mean, the mode, and the median of the data set?
56; 56; 56; 58; 59; 60; 62; 64; 64; 65; 67

Sandile Ndlovu

Numerade Educator

Problem 67

Of the three measures, which tends to reflect skewing the most, the mean, the mode, or the median? Why?

Sandile Ndlovu

Numerade Educator

Problem 68

In a perfectly symmetrical distribution, when would the mode be different from the mean and median?

Sandile Ndlovu

Numerade Educator

Problem 69

Use the following information to answer the next two exercises: The following data are the distances between 20 retail stores and a large distribution center. The distances are in miles.
29; 37; 38; 40; 58; 67; 68; 69; 76; 86; 87; 95; 96; 96; 99; 106; 112; 127; 145; 150
Use a graphing calculator or computer to find the standard deviation and round to the nearest tenth.

Sandile Ndlovu

Numerade Educator

Problem 70

Use the following information to answer the next two exercises: The following data are the distances between 20 retail stores and a large distribution center. The distances are in miles.
29; 37; 38; 40; 58; 67; 68; 69; 76; 86; 87; 95; 96; 96; 99; 106; 112; 127; 145; 150
Find the value that is one standard deviation below the mean.

Sandile Ndlovu

Numerade Educator

Problem 71

Use the following information to answer the next two exercises: The following data are the distances between 20 retail stores and a large distribution center. The distances are in miles.
29; 37; 38; 40; 58; 67; 68; 69; 76; 86; 87; 95; 96; 96; 99; 106; 112; 127; 145; 150
Two baseball players, Fredo and Karl, on different teams wanted to find out who had the higher batting average when compared to his team. Which baseball player had the higher batting average when compared to his team?

Sandile Ndlovu

Numerade Educator

Problem 72

$$\begin{array}{|l|l|l|}\hline \text { Baseball Player } & {\text { Batting Average }} & {\text { Team Batting Average }} & {\text { Team Standard Deviation }} \\ \hline \text { Fredo } & {0.158} & {0.166} & {0.012} \\ \hline \text { Karl } & {0.177} & {0.189} & {0.015} \\ \hline\end{array}$$
Use Table 2.57 to find the value that is three standard deviations:
a. above the mean
b. below the mean

Dani Dutmer

Numerade Educator

Problem 73

Find the standard deviation for the following frequency tables using the formula. Check the calculations with the TI 83/84.
Find the standard deviation for the following frequency tables using the formula. Check the calculations with the TI 83/84.
a. (TABLE CAN'T COPY)
b. (TABLE CAN'T COPY)
c. (TABLE CAN'T COPY)

Sandile Ndlovu

Numerade Educator

Problem 74

Student grades on a chemistry exam were: 77, 78, 76, 81, 86, 51, 79, 82, 84, 99
a. Construct a stem-and-leaf plot of the data.
b. Are there any potential outliers? If so, which scores are they? Why do you consider them outliers?

Sandile Ndlovu

Numerade Educator

Problem 75

Table 2.61 contains the 2010 obesity rates in U.S. states and Washington, DC.
(TABLE CAN'T COPY)
a. Use a random number generator to randomly pick eight states. Construct a bar graph of the obesity rates of those eight states.
b. Construct a bar graph for all the states beginning with the letter "A."
c. Construct a bar graph for all the states beginning with the letter "M."

Jerelyn Nevil

Numerade Educator

Problem 76

Suppose that three book publishers were interested in the number of fiction paperbacks adult consumers purchase per month. Each publisher conducted a survey. In the survey, adult consumers were asked the number of fiction paperbacks they had purchased the previous month. The results are as follows:
$$\begin{array}{|l|l|}\hline \# \text { of books } & {\text { Freq. }} & {\text { Rel. Freq. }} \\ \hline 0 & {10} \\ \hline 1 & {12} \\ \hline 2 & {12} \\ \hline 2 & {16} \\ \hline 3 & {12} \\ \hline 4 & {8} \\ \hline 5 & {6} \\ \hline 6 & {2} \\ \hline 8 & {2} \\ \hline\end{array}$$
Table 2.62 Publisher A
$$\begin{array}{|l|l|l|}\hline \# \text { of books } & {\text { Freq. }} & {\text { Rel. Freq. }} \\ \hline 0 & {18} \\ \hline 1 & {24} \\ \hline 2 & {24} \\ \hline 3 & {22} \\ \hline 3 & {22} \\ \hline 5 & {10} \\ \hline 7 & {5} \\ \hline 9 & {1} \\ \hline\end{array}$$
Table 2.63 Publisher B
$$\begin{array}{|l|l|l|}\hline \text { of books } & {\text { Freq. }} & {\text { Rel. Freq. }} \\ \hline 0-1 & {20} \\ \hline 2-3 & {35} \\ \hline 4-5 & {12} \\ \hline 6-7 & {2} \\ \hline 8-9 & {1} \\ \hline\end{array}$$
Table 2.64 Publisher C

a. Find the relative frequencies for each survey. Write them in the charts.
b. Using either a graphing calculator, computer, or by hand, use the frequency column to construct a histogram for each publisher's survey. For Publishers A and B, make bar widths of one. For Publisher C, make bar widths of two.
c. In complete sentences, give two reasons why the graphs for Publishers A and B are not identical.
d. Would you have expected the graph for Publisher C to look like the other two graphs? Why or why not?
e. Make new histograms for Publisher A and Publisher B. This time, make bar widths of two.
f. Now, compare the graph for Publisher C to the new graphs for Publishers A and B. Are the graphs more similar or more different? Explain your answer.

Alexander Cheng

Alexander Cheng

Numerade Educator

Problem 77

Often, cruise ships conduct all on-board transactions, with the exception of gambling, on a cashless basis. At the end of the cruise, guests pay one bill that covers all onboard transactions. Suppose that 60 single travelers and 70 couples were surveyed as to their on-board bills for a seven-day cruise from Los Angeles to the Mexican Riviera. Following is a summary of the bills for each group.
(TABLE CAN'T COPY)
a. Fill in the relative frequency for each group.
b. Construct a histogram for the singles group. Scale the $x$ -axis by $\$ 50$ widths. Us $\$ 50$ widths. Use relative frequency on the $y$ -axis.
c. Construct a histogram for the couples group. Scale the $x$ -axis by $\$ 50$ widths. Use relative frequency on the $y$ -axis.
d. Compare the two graphs:
$$\begin{array}{l}{\text { i. List two similarities between the graphs. }} \\ {\text { ii. List two differences between the graphs. }} \\ {\text { iii. Overall, are the graphs more similar or different? }}\end{array}$$
e. Construct a new graph for the couples by hand. Since each couple is paying for two individuals, instead of scaling the $x$ -axis by $\$ 50,$ scale it by $\$ 100 .$ Use relative frequency on the $y$ -axis.
f. Compare the graph for the singles with the new graph for the couples:
$$\begin{array}{l}{\text { i. List two similarities between the graphs. }} \\ {\text { ii. Overall, are the graphs more similar or different? }}\end{array}$$
g. How did scaling the couples graph differently change the way you compared it to the singles graph?
h. Based on the graphs, do you think that individuals spend the same amount, more or less, as singles as they do person by person as a couple? Explain why in one or two complete sentences.

Teresa Wray

Numerade Educator

Problem 78

Twenty-five randomly selected students were asked the number of movies they watched the previous week. The results are as follows.
(TABLE CAN'T COPY)
a. Construct a histogram of the data.
b. Complete the columns of the chart.

Sandile Ndlovu

Numerade Educator

Problem 79

Use the following information to answer the next two exercises: Suppose one hundred eleven people who shopped in a special t-shirt store were asked the number of t-shirts they own costing more than $19 each.
(GRAPH CAN'T COPY)
The percentage of people who own at most three t-shirts costing more than $19 each is approximately:
a. 21
b. 59
c. 41
d. Cannot be determined

Sandile Ndlovu

Numerade Educator

Problem 80

Use the following information to answer the next two exercises: Suppose one hundred eleven people who shopped in a special t-shirt store were asked the number of t-shirts they own costing more than $19 each.
(GRAPH CAN'T COPY)
If the data were collected by asking the first 111 people who entered the store, then the type of sampling is:
a. cluster
b. simple random
c. stratified
d. convenience

Sandile Ndlovu

Numerade Educator

Problem 81

Following are the 2010 obesity rates by U.S. states and Washington, DC.
(TABLE CAN'T COPY)

Sandile Ndlovu

Numerade Educator

Problem 82

The median age for U.S. blacks currently is 30.9 years; for U.S. whites it is 42.3 years.
a. Based upon this information, give two reasons why the black median age could be lower than the white median age.
b. Does the lower median age for blacks necessarily mean that blacks die younger than whites? Why or why not?
c. How might it be possible for blacks and whites to die at approximately the same age, but for the median age for whites to be higher?

Sandile Ndlovu

Numerade Educator

Problem 83

Six hundred adult Americans were asked by telephone poll, "What do you think constitutes a middle-class income?" The results are in Table 2.69. Also, include left endpoint, but not the right endpoint.
(TABLE CAN'T COPY)
a. What percentage of the survey answered "not sure"?
b. What percentage think that middle-class is from $25,000 to $50,000?
c. Construct a histogram of the data.
i. Should all bars have the same width, based on the data? Why or why not?
ii. How should the <20,000 and the 100,000+ intervals be handled? Why?
d. Find the 40th and 80th percentiles
e. Construct a bar graph of the data

Oluwadamilola Ameobi

Oluwadamilola Ameobi

Numerade Educator

Problem 84

Given the following box plot:
(FIGURE CAN'T COPY)
a. which quarter has the smallest spread of data? What is that spread?
b. which quarter has the largest spread of data? What is that spread?
c. find the interquartile range (IQR).
d. are there more data in the interval 5–10 or in the interval 10–13? How do you know this?
e. which interval has the fewest data in it? How do you know this?
$$
\begin{array}{l}{\text { i. } 0-2} \\ {\text { ii. } 2-4} \\ {\text { iii. } 10-12} \\ {\text { iV. } 12-13} \\ {\text { V. need more information }}\end{array}
$$

Sandile Ndlovu

Numerade Educator

Problem 85

The following box plot shows the U.S. population for 1990, the latest available year.
(FIGURE CAN'T COPY)
a. Are there fewer or more children (age 17 and under) than senior citizens (age 65 and over)? How do you know?
b. 12.6% are age 65 and over. Approximately what percentage of the population are working age adults (above age 17 to age 65)?

Marc Lauzon

Numerade Educator

Problem 86

In a survey of 20-year-olds in China, Germany, and the United States, people were asked the number of foreign countries they had visited in their lifetime. The following box plots display the results.
(FIGURE CAN'T COPY)
a. In complete sentences, describe what the shape of each box plot implies about the distribution of the data collected.
b. Have more Americans or more Germans surveyed been to over eight foreign countries?
c. Compare the three box plots. What do they imply about the foreign travel of 20-year-old residents of the three countries when compared to each other?

Sandile Ndlovu

Numerade Educator

Problem 87

Given the following box plot, answer the questions.
(FIGURE CAN'T COPY)
a. Think of an example (in words) where the data might fit into the above box plot. In 2–5 sentences, write down the example.
b. What does it mean to have the first and second quartiles so close together, while the second to third quartiles are far apart?

Sandile Ndlovu

Numerade Educator

Problem 88

Given the following box plots, answer the questions.
(FIGURE CAN'T COPY)
a. In complete sentences, explain why each statement is false.
$$\begin{array}{l}{\text { i. Data } 1 \text { has more data values above two than Data } 2 \text { has above two. }} \\ {\text { ii. The data sets cannot have the same mode. }} \\ {\text { iii. For Data } 1, \text { there are more data values below four than there are above four. }}\end{array}$$
b. For which group, Data 1 or Data 2, is the value of “7” more likely to be an outlier? Explain why in complete sentences.

Sandile Ndlovu

Numerade Educator

Problem 89

A survey was conducted of 130 purchasers of new BMW 3 series cars, 130 purchasers of new BMW 5 series cars, and 130 purchasers of new BMW 7 series cars. In it, people were asked the age they were when they purchased their car. The following box plots display the results.
(FIGURE CAN'T COPY)
a. In complete sentences, describe what the shape of each box plot implies about the distribution of the data collected for that car series.
b. Which group is most likely to have an outlier? Explain how you determined that.
c. Compare the three box plots. What do they imply about the age of purchasing a BMW from the series when
compared to each other?
d. Look at the BMW 5 series. Which quarter has the smallest spread of data? What is the spread?
e. Look at the BMW 5 series. Which quarter has the largest spread of data? What is the spread?
f. Look at the BMW 5 series. Estimate the interquartile range (IQR).
g. Look at the BMW 5 series. Are there more data in the interval 31 to 38 or in the interval 45 to 55? How do you know this?
h. Look at the BMW 5 series. Which interval has the fewest data in it? How do you know this?
$$\begin{array}{l}{\text { i. } 31-35} \\ {\text { ii. } 38-41} \\ {\text { iii. } 41-64}\end{array}$$

Gus Steppen

Numerade Educator

Problem 90

Twenty-five randomly selected students were asked the number of movies they watched the previous week. The results are as follows:
$$\begin{array}{|l|l|}\hline \# \text { of movies } & {\text { Frequency }} \\ \hline 0 & {5} \\ \hline 1 & {9} \\ \hline 2 & {6} \\ \hline 3 & {4} \\ \hline 4 & {1} \\ \hline\end{array}$$
Table 2.70

Sandile Ndlovu

Numerade Educator

Problem 91

The most obese countries in the world have obesity rates that range from 11.4$\%$ to 74.6$\%$ . This data is summarized in the following table.
(TABLE CAN'T COPY)
a. What is the best estimate of the average obesity percentage for these countries?
b. The United States has an average obesity rate of 33.9%. Is this rate above average or below?
c. How does the United States compare to other countries?

Sandile Ndlovu

Numerade Educator

Problem 92

Table 2.72 gives the percent of children under five considered to be underweight. What is the best estimate for the mean percentage of underweight children?
(TABLE CAN'T COPY)

Sandile Ndlovu

Numerade Educator

Problem 93

The median age of the U.S. population in 1980 was 30.0 years. In 1991, the median age was 33.1 years.
a. What does it mean for the median age to rise?
b. Give two reasons why the median age could rise.
c. For the median age to rise, is the actual number of children less in 1991 than it was in 1980? Why or why not?

Sandile Ndlovu

Numerade Educator

Problem 94

Use the following information to answer the next nine exercises: The population parameters below describe the full-time equivalent number of students (FTES) each year at Lake Tahoe Community College from 1976–1977 through 2004–2005.
$\bullet \mu=1000 \mathrm{FTES}$
$\bullet$ median $=1,014 \mathrm{FTES}$
$\bullet \quad \sigma=474 \mathrm{FTES}$
$\cdot$ first quartile $=528.5$ FTES
$\cdot$ third quartile $=1,447.5$ FTES
$\cdot n=29$ years
A sample of 11 years is taken. About how many are expected to have a FTES of 1014 or above? Explain how you determined your answer.

Sandile Ndlovu

Numerade Educator

Problem 95

Use the following information to answer the next nine exercises: The population parameters below describe the full-time equivalent number of students (FTES) each year at Lake Tahoe Community College from 1976–1977 through 2004–2005.
$\bullet \mu=1000 \mathrm{FTES}$
$\bullet$ median $=1,014 \mathrm{FTES}$
$\bullet \quad \sigma=474 \mathrm{FTES}$
$\cdot$ first quartile $=528.5$ FTES
$\cdot$ third quartile $=1,447.5$ FTES
$\cdot n=29$ years
75$\%$ of all years have an FTES:
a. at or below: ____
b. at or above: ____

Sandile Ndlovu

Numerade Educator

Problem 96

Use the following information to answer the next nine exercises: The population parameters below describe the full-time equivalent number of students (FTES) each year at Lake Tahoe Community College from 1976–1977 through 2004–2005.
$\bullet \mu=1000 \mathrm{FTES}$
$\bullet$ median $=1,014 \mathrm{FTES}$
$\bullet \quad \sigma=474 \mathrm{FTES}$
$\cdot$ first quartile $=528.5$ FTES
$\cdot$ third quartile $=1,447.5$ FTES
$\cdot n=29$ years
The population standard deviation $=$ ____

Sandile Ndlovu

Numerade Educator

Problem 97

Use the following information to answer the next nine exercises: The population parameters below describe the full-time equivalent number of students (FTES) each year at Lake Tahoe Community College from 1976–1977 through 2004–2005.
$\bullet \mu=1000 \mathrm{FTES}$
$\bullet$ median $=1,014 \mathrm{FTES}$
$\bullet \quad \sigma=474 \mathrm{FTES}$
$\cdot$ first quartile $=528.5$ FTES
$\cdot$ third quartile $=1,447.5$ FTES
$\cdot n=29$ years
What percent of the FTES were from 528.5 to 1447.5? How do you know?

Sandile Ndlovu

Numerade Educator

Problem 98

Use the following information to answer the next nine exercises: The population parameters below describe the full-time equivalent number of students (FTES) each year at Lake Tahoe Community College from 1976–1977 through 2004–2005.
$\bullet \mu=1000 \mathrm{FTES}$
$\bullet$ median $=1,014 \mathrm{FTES}$
$\bullet \quad \sigma=474 \mathrm{FTES}$
$\cdot$ first quartile $=528.5$ FTES
$\cdot$ third quartile $=1,447.5$ FTES
$\cdot n=29$ years
What is the IQR? What does the IQR represent?

Sandile Ndlovu

Numerade Educator

Problem 99

Use the following information to answer the next nine exercises: The population parameters below describe the full-time equivalent number of students (FTES) each year at Lake Tahoe Community College from 1976–1977 through 2004–2005.
$\bullet \mu=1000 \mathrm{FTES}$
$\bullet$ median $=1,014 \mathrm{FTES}$
$\bullet \quad \sigma=474 \mathrm{FTES}$
$\cdot$ first quartile $=528.5$ FTES
$\cdot$ third quartile $=1,447.5$ FTES
$\cdot n=29$ years
How many standard deviations away from the mean is the median?

Sandile Ndlovu

Numerade Educator

Problem 100

Use the following information to answer the next nine exercises: The population parameters below describe the full-time equivalent number of students (FTES) each year at Lake Tahoe Community College from 1976–1977 through 2004–2005.
$\bullet \mu=1000 \mathrm{FTES}$
$\bullet$ median $=1,014 \mathrm{FTES}$
$\bullet \quad \sigma=474 \mathrm{FTES}$
$\cdot$ first quartile $=528.5$ FTES
$\cdot$ third quartile $=1,447.5$ FTES
$\cdot n=29$ years
Additional Information: The population FTES for 2005–2006 through 2010–2011 was given in an updated report. The data are reported here.
(TABLE CAN'T COPY)
Calculate the mean, median, standard deviation, the first quartile, the third quartile and the IQR. Round to one decimal place.

Sandile Ndlovu

Numerade Educator

Problem 101

Use the following information to answer the next nine exercises: The population parameters below describe the full-time equivalent number of students (FTES) each year at Lake Tahoe Community College from 1976–1977 through 2004–2005.
$\bullet \mu=1000 \mathrm{FTES}$
$\bullet$ median $=1,014 \mathrm{FTES}$
$\bullet \quad \sigma=474 \mathrm{FTES}$
$\cdot$ first quartile $=528.5$ FTES
$\cdot$ third quartile $=1,447.5$ FTES
$\cdot n=29$ years
Additional Information: The population FTES for 2005–2006 through 2010–2011 was given in an updated report. The data are reported here.
(TABLE CAN'T COPY)
Construct a box plot for the FTES for 2005–2006 through 2010–2011 and a box plot for the FTES for 1976–1977 through 2004–2005.

Sandile Ndlovu

Numerade Educator

Problem 102

Use the following information to answer the next nine exercises: The population parameters below describe the full-time equivalent number of students (FTES) each year at Lake Tahoe Community College from 1976–1977 through 2004–2005.
$\bullet \mu=1000 \mathrm{FTES}$
$\bullet$ median $=1,014 \mathrm{FTES}$
$\bullet \quad \sigma=474 \mathrm{FTES}$
$\cdot$ first quartile $=528.5$ FTES
$\cdot$ third quartile $=1,447.5$ FTES
$\cdot n=29$ years
Additional Information: The population FTES for 2005–2006 through 2010–2011 was given in an updated report. The data are reported here.
(TABLE CAN'T COPY)
Compare the IQR for the FTES for 1976–77 through 2004–2005 with the IQR for the FTES for 2005-2006 through 2010–2011. Why do you suppose the IQRs are so different?

Sandile Ndlovu

Numerade Educator

Problem 103

Three students were applying to the same graduate school. They came from schools with different grading systems. Which student had the best GPA when compared to other students at his school? Explain how you determined your answer.
(TABLE CAN'T COPY)

Sandile Ndlovu

Numerade Educator

Problem 104

A music school has budgeted to purchase three musical instruments. They plan to purchase a piano costing $\$ 3,000,$ a guitar costing $\$ 550,$ and a drum set costing $\$ 600 .$ The mean cost for a piano is $\$ 4,000$ with a standard deviation of $\$ 2,500$ . The mean cost for a guitar is $\$ 500$ with a standard deviation of $\$ 200$ . The mean cost for drums is $\$ 700$ with a standard deviation of $\$ 100$ . Which cost is the lowest, when compared to other instruments of the same type? Which cost is the highest when compared to other instruments of the same type. Justify your answer.

Sandile Ndlovu

Numerade Educator

Problem 105

An elementary school class ran one mile with a mean of 11 minutes and a standard deviation of three minutes. Rachel, a student in the class, ran one mile in eight minutes. A junior high school class ran one mile with a mean of nine minutes and a standard deviation of two minutes. Kenji, a student in the class, ran 1 mile in 8.5 minutes. A high school class ran one mile with a mean of seven minutes and a standard deviation of four minutes. Nedda, a student in the class, ran one mile in eight minutes.
a. Why is Kenji considered a better runner than Nedda, even though Nedda ran faster than he?
b. Who is the fastest runner with respect to his or her class? Explain why.

Sandile Ndlovu

Numerade Educator

Problem 106

The most obese countries in the world have obesity rates that range from 11.4$\%$ to 74.6$\%$ . This data is summarized in Table $14 .$
(TABLE CAN'T COPY)
What is the best estimate of the average obesity percentage for these countries? What is the standard deviation for the listed obesity rates? The United States has an average obesity rate of 33.9%. Is this rate above average or below? How “unusual” is the United States’ obesity rate compared to the average rate? Explain.

Sandile Ndlovu

Numerade Educator

Problem 107

Table 2.76 gives the percent of children under five considered to be underweight.
(TABLE CAN'T COPY)
What is the best estimate for the mean percentage of underweight children? What is the standard deviation? Which interval(s) could be considered unusual? Explain.

Sandile Ndlovu

Numerade Educator

Problem 108

Santa Clara County, CA, has approximately 27,873 Japanese-Americans. Their ages are as follows:
$$\begin{array}{|l|l|}\hline \text { Age Group } & {\text { Percent of Community }} \\ \hline 0-17 & {18.9} \\ \hline 18-24 & {8.0} \\ \hline 25-34 & {22.8} \\ \hline 35-44 & {15.8} \\ \hline 45-54 & {13.1} \\ \hline 55-64 & {11.9} \\ \hline 65+& {10.3} \\ \hline\end{array}$$
a. Construct a histogram of the Japanese-American community in Santa Clara County, CA. The bars will not be the same width for this example. Why not? What impact does this have on the reliability of the graph?
b. What percentage of the community is under age 35?
c. Which box plot most resembles the information above?
(FIGURE CAN'T COPY)

Alexander Cheng

Alexander Cheng

Numerade Educator

Problem 109

Javier and Ercilia are supervisors at a shopping mall. Each was given the task of estimating the mean distance that shoppers live from the mall. They each randomly surveyed 100 shoppers. The samples yielded the following information.
(TABLE CAN'T COPY)
a. How can you determine which survey was correct ?
b. Explain what the difference in the results of the surveys implies about the data.
c. If the two histograms depict the distribution of values for each supervisor, which one depicts Ercilia's sample? How do you know?
(FIGURE CAN'T COPY)
d. If the two box plots depict the distribution of values for each supervisor, which one depicts Ercilia’s sample? How do you know?
(FIGURE CAN'T COPY)

Sandile Ndlovu

Numerade Educator

Problem 110

Use the following information to answer the next three exercises: We are interested in the number of years students in a particular elementary statistics class have lived in California. The information in the following table is from the entire section.
(TABLE CAN'T COPY)
What is the IQR?
a. 8
b. 11
c. 15
d. 35

Sandile Ndlovu

Numerade Educator

Problem 111

Use the following information to answer the next three exercises: We are interested in the number of years students in a particular elementary statistics class have lived in California. The information in the following table is from the entire section.
(TABLE CAN'T COPY)
What is the mode?
a. 19
b. 19.5
c. 14 and 20
d. 22.65

Sandile Ndlovu

Numerade Educator

Problem 112

Use the following information to answer the next three exercises: We are interested in the number of years students in a particular elementary statistics class have lived in California. The information in the following table is from the entire section.
(TABLE CAN'T COPY)
Is this a sample or the entire population?
a. sample
b. entire population
c. neither

Sandile Ndlovu

Numerade Educator

Problem 113

Twenty-five randomly selected students were asked the number of movies they watched the previous week. The results are as follows:
$$\begin{array}{|l|l|}\hline \# \text { of movies } & {\text { Frequency }} \\ \hline 0 & {5} \\ \hline 1 & {9} \\ \hline 2 & {6} \\ \hline 3 & {4} \\ \hline 4 & {1} \\ \hline\end{array}$$
a. Find the sample mean $\overline{x}$ .
b. Find the approximate sample standard deviation, s.

Sandile Ndlovu

Numerade Educator

Problem 114

Forty randomly selected students were asked the number of pairs of sneakers they owned. Let $X=$ the number of pairs of sneakers owned.The results are as follows:
$$\begin{array}{|l|l|}\hline X & {\text { Frequency }} \\ \hline 1 & {2} \\ \hline 2 & {5} \\ \hline 3 & {8} \\ \hline 4 & {12} \\ \hline 5 & {12} \\ \hline 6 & {0} \\ \hline 7 & {1} \\ \hline\end{array}$$
a. Find the sample mean $\overline{x}$
b. Find the sample standard deviation, s
c. Construct a histogram of the data.
d. Complete the columns of the chart.
e. Find the first quartile.
f. Find the median.
g. Find the third quartile.
h. Construct a box plot of the data.
i. What percent of the students owned at least five pairs?
j. Find the $40^{\text { th }}$ percentile.
k. Find the $90^{\text { th }}$ percentile.
I. Construct a line graph of the data
m. Construct a stemplot of the data

Jerelyn Nevil

Numerade Educator

Problem 115

Following are the published weights (in pounds) of all of the team members of the San Francisco 49ers from a previous year.
177; 205; 210; 210; 232; 205; 185; 185; 178; 210; 206; 212; 184; 174; 185; 242; 188; 212; 215; 247; 241; 223; 220; 260; 245; 259; 278; 270; 280; 295; 275; 285; 290; 272; 273; 280; 285; 286; 200; 215; 185; 230; 250; 241; 190; 260; 250; 302; 265; 290; 276; 228; 265
a. Organize the data from smallest to largest value.
b. Find the median.
c. Find the first quartile.
d. Find the third quartile.
e. Construct a box plot of the data.
f. The middle 50$\%$ of the weights are from ____ to ____ .
g. If our population were all professional football players, would the above data be a sample of weights or the population of weights? Why?
h. If our population included every team member who ever played for the San Francisco 49ers, would the above data be a sample of weights or the population of weights? Why?
i. Assume the population was the San Francisco 49ers. Find:
$$\begin{array}{l}{\text { i. the population mean, } \mu} \\ {\text { ii. the population standard deviation, } \sigma \text { . }} \\ {\text { iii. the weight that is two standard deviations below the mean. }} \\ {\text { iv. When Steve Young, quarterback, played football, he weighed 205 pounds. How many standard }} \\ {\text { deviations above or below the mean was he? }}\end{array}$$
j. That same year, the mean weight for the Dallas Cowboys was 240.08 pounds with a standard deviation of 44.38 pounds. Emmit Smith weighed in at 209 pounds. With respect to his team, who was lighter, Smith or Young? How did you determine your answer?

Bryan Meares

Numerade Educator

Problem 116

One hundred teachers attended a seminar on mathematical problem solving. The attitudes of a representative sample of 12 of the teachers were measured before and after the seminar. A positive number for change in attitude indicates that a teacher's attitude toward math became more positive. The 12 change scores are as follows:
3; 8; –1; 2; 0; 5; –3; 1; –1; 6; 5; –2
a. What is the mean change score?
b. What is the standard deviation for this population?
c. What is the median change score?
d. Find the change score that is 2.2 standard deviations below the mean.

Sandile Ndlovu

Numerade Educator

Problem 117

Refer to Figure 2.50 determine which of the following are true and which are false. Explain your solution to each part in complete sentences.
(FIGURE CAN'T COPY)
a. The medians for all three graphs are the same.
b. We cannot determine if any of the means for the three graphs is different.
c. The standard deviation for graph b is larger than the standard deviation for graph a.
d. We cannot determine if any of the third quartiles for the three graphs is different.

Sandile Ndlovu

Numerade Educator

Problem 118

In a recent issue of the IEEE Spectrum, 84 engineering conferences were announced. Four conferences lasted two days. Thirty-six lasted three days. Eighteen lasted four days. Nineteen lasted five days. Four lasted six days. One lasted seven days. One lasted eight days. One lasted nine days. Let $X=$ the length (in days) of an engineering conference.
a. Organize the data in a chart.
b. Find the median, the first quartile, and the third quartile.
c. Find the 65th percentile.
d. Find the 10th percentile.
e. Construct a box plot of the data.
f. The middle 50$\%$ of the conferences last from _____ days to _____ days.
g. Calculate the sample mean of days of engineering conferences.
h. Calculate the sample standard deviation of days of engineering conferences.
i. Find the mode.
j. If you were planning an engineering conference, which would you choose as the length of the conference: mean; median; or mode? Explain why you made that choice.
k. Give two reasons why you think that three to five days seem to be popular lengths of engineering conferences.

Alexander Cheng

Alexander Cheng

Numerade Educator

Problem 119

A survey of enrollment at 35 community colleges across the United States yielded the following figures:
6414; 1550; 2109; 9350; 21828; 4300; 5944; 5722; 2825; 2044; 5481; 5200; 5853; 2750; 10012; 6357; 27000; 9414; 7681; 3200; 17500; 9200; 7380; 18314; 6557; 13713; 17768; 7493; 2771; 2861; 1263; 7285; 28165; 5080; 11622
a. Organize the data into a chart with five intervals of equal width. Label the two columns "Enrollment" and "Frequency."
b. Construct a histogram of the data.
c. If you were to build a new community college, which piece of information would be more valuable: the mode or the mean?
d. Calculate the sample mean.
e. Calculate the sample standard deviation.
f. A school with an enrollment of 8000 would be how many standard deviations away from the mean?

Kerri Mccallon

Numerade Educator

Problem 120

Use the following information to answer the next two exercises. X = the number of days per week that 100 clients use a particular exercise facility.
$$\begin{array}{|l|l|}\hline x & {\text { Frequency }} \\ \hline 0 & {3} \\ \hline 1 & {12} \\ \hline 2 & {33} \\ \hline 3 & {28} \\ \hline 4 & {11} \\ \hline 5 & {9} \\ \hline 6 & {4} \\ \hline\end{array}$$
The $80^{\text { th }}$ percentile is ____
a. 5
b. 80
c. 3
d. 4

Sandile Ndlovu

Numerade Educator

Problem 121

Use the following information to answer the next two exercises. X = the number of days per week that 100 clients use a particular exercise facility.
$$\begin{array}{|l|l|}\hline x & {\text { Frequency }} \\ \hline 0 & {3} \\ \hline 1 & {12} \\ \hline 2 & {33} \\ \hline 3 & {28} \\ \hline 4 & {11} \\ \hline 5 & {9} \\ \hline 6 & {4} \\ \hline\end{array}$$
The number that is 1.5 standard deviations BELOW the mean is approximately _____
a. 0.7
b. 4.8
c. $-2.8$
d. Cannot be determined

Sandile Ndlovu

Numerade Educator

Problem 122

Suppose that a publisher conducted a survey asking adult consumers the number of fiction paperback books they had purchased in the previous month. The results are summarized in the Table 2.83.
$$\begin{array}{|l|l|}\hline \# \text { of books } & {\text { Freq. }} & {\text { Rel. Freq. }} \\ \hline 0 & {18} \\ \hline 1 & {24} \\ \hline 2 & {24} \\ \hline 3 & {22} \\ \hline 4 & {15} \\ \hline 5 & {5} \\ \hline 7 & {5} \\ \hline 9 & {1} \\ \hline\end{array}$$
a. Are there any outliers in the data? Use an appropriate numerical test involving the IQR to identify outliers, if any, and clearly state your conclusion.
b. If a data value is identified as an outlier, what should be done about it?
c. Are any data values further than two standard deviations away from the mean? In some situations, statisticians may use this criteria to identify data values that are unusual, compared to the other data values. (Note that this criteria is most appropriate to use for data that is mound-shaped and symmetric, rather than for skewed data.)
d. Do parts a and c of this problem give the same answer?
e. Examine the shape of the data. Which part, a or c, of this question gives a more appropriate result for this data?
f. Based on the shape of the data which is the most appropriate measure of center for this data: mean, median or mode?

Dela Akpalu

Numerade Educator