Algebra

Holliday, Luchin, Cuevas, Carter Marks, Day, Casey, Hayek

Chapter 12

Probability and Statistics - all with Video Answers

Educators

Section 6

Statistical Measures

Problem 1

The table below shows the amounts of money spent on education per student in a recent year in two regions of the United States.
$$\begin{array}{|c|c|c|c|}\hline \text { Alaska } & {9564} & {\text { Texas }} & {6771} \\ \hline \text { California } & {7405} & {\text { Arkansas }} & {6276} \\ \hline \text { Washington } & {7039} & {\text { Louisiana }} & {6567} \\ \hline \text { Oregon } & {7642} & {\text { Oklahoma }} & {6299} \\ \hline\end{array}$$
Find the mean for each region.

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Problem 2

The table below shows the amounts of money spent on education per student in a recent year in two regions of the United States.
$$\begin{array}{|c|c|c|c|}\hline \text { Alaska } & {9564} & {\text { Texas }} & {6771} \\ \hline \text { California } & {7405} & {\text { Arkansas }} & {6276} \\ \hline \text { Washington } & {7039} & {\text { Louisiana }} & {6567} \\ \hline \text { Oregon } & {7642} & {\text { Oklahoma }} & {6299} \\ \hline\end{array}$$
For which region is the mean more representative of the data? Explain.

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Problem 3

Find the variance and standard deviation of each set of data to the nearest tenth.
{48, 36, 40, 29, 45, 51, 38, 47, 39, 37}

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Problem 4

Find the variance and standard deviation of each set of data to the nearest tenth.
{321, 322, 323, 324, 325, 326, 327, 328, 329, 330}

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Problem 5

Find the variance and standard deviation of each set of data to the nearest tenth.
{43, 56, 78, 81, 47, 42, 34, 22, 78, 98, 38, 46, 54, 67, 58, 92, 55}

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Problem 6

Find the variance and standard deviation of each set of data to the nearest tenth.
{400, 300, 325, 275, 425, 375, 350}

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Problem 7

Find the variance and standard deviation of each set of data to the nearest tenth.
{5, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 9}

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Problem 8

Find the variance and standard deviation of each set of data to the nearest tenth.
{2.4, 5.6, 1.9, 7.1, 4.3, 2.7, 4.6, 1.8, 2.4}

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Problem 9

Find the variance and standard deviation of each set of data to the nearest tenth.
{4.3, 6.4, 2.9, 3.1, 8.7, 2.8, 3.6, 1.9, 7.2}

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Problem 10

Find the variance and standard deviation of each set of data to the nearest tenth.
{234, 345, 123, 368, 279, 876, 456, 235, 333, 444}

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Problem 11

Find the variance and standard deviation of each set of data to the nearest tenth.
{13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 67, 56, 34, 99, 44, 55}

Check back soon!

Problem 12

Stem $\qquad$ Leaf
4 $\qquad$ 4 5 6 7 7
5 $\qquad$ 3 5 6 7 8 9
6 $\qquad$ 7 7 8 9 9 9 $\quad$ 4 \ 5 = 45

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Problem 13

Stem Leaf
5 $\qquad$ 7 7 7 8 9
6 $\qquad$ 3 4 5 5 6 7
7 $\qquad$ 2 3 4 5 6 $\qquad$ 6 \ 3 = 63

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Problem 14

The table below shows the rebounding totals for the members of the 2005 Charlotte Sting.
$$\begin{array}{|l|l|l|l|l|l|l|l|l|l|}\hline 162 & {145} & {179} & {37} & {44} & {53} & {70} & {65} & {47} & {35} & {71} & {5} & {5} \\ \hline\end{array}$$
Find the mean, median, and mode of the data to the nearest tenth.

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Problem 15

The table below shows the rebounding totals for the members of the 2005 Charlotte Sting.
$$\begin{array}{|l|l|l|l|l|l|l|l|l|l|}\hline 162 & {145} & {179} & {37} & {44} & {53} & {70} & {65} & {47} & {35} & {71} & {5} & {5} \\ \hline\end{array}$$
Which measure of central tendency best represents the data? Explain your answer.

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Problem 16

An electronics store placed an ad in the newspaper showing five flat-screen TVs for sale. The ad says, "Our flat-screen TVs average $\$ 695 . "$ The prices of the flat- screen TVs are $\$ 1200, \$ 999, \$ 1499, \$ 695, \$ 695, \$ 1100, \$ 1300,$ and $\$ 695 .$
Find the mean, median, and mode of the prices.

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Problem 17

An electronics store placed an ad in the newspaper showing five flat-screen TVs for sale. The ad says, "Our flat-screen TVs average $\$ 695 . "$ The prices of the flat- screen TVs are $\$ 1200, \$ 999, \$ 1499, \$ 695, \$ 695, \$ 1100, \$ 1300,$ and $\$ 695 .$
Which measure is the store using in its ad? Why did they choose it?

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Problem 18

An electronics store placed an ad in the newspaper showing five flat-screen TVs for sale. The ad says, "Our flat-screen TVs average $\$ 695 . "$ The prices of the flat- screen TVs are $\$ 1200, \$ 999, \$ 1499, \$ 695, \$ 695, \$ 1100, \$ 1300,$ and $\$ 695 .$
As a consumer, which measure would you want to see advertised? Explain.

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Problem 19

The Millersburg school board is negotiating a pay raise with the teacher's union. Three of the administrators have salaries of $\$ 90,000$ each. However, a majority of the teachers have salaries of about $\$ 45,000$ per year.
You are a member of the school board and would like to show that the current salaries are reasonable. Would you quote the mean, median, or mode as the “average” salary to justify your claim? Explain.

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Problem 20

The Millersburg school board is negotiating a pay raise with the teacher's union. Three of the administrators have salaries of $\$ 90,000$ each. However, a majority of the teachers have salaries of about $\$ 45,000$ per year.
You are the head of the teacher’s union and maintain that a pay raise is in order. Which of the mean, median, or mode would you quote to justify your claim? Explain your reasoning.

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Problem 21

The table lists the areas of some large shopping malls in the United States.
Mall $\qquad$ Gross Leasable Area $\left(\mathrm{ft}^{2}\right)$
1 Del Amo Fashion Center, Torrance, CA 3,000,000
2 South Coast Plaza/Crystal Court, Costa Mesa, CA 2,918,236
3 Mall of America, Bloomington, MN 2,472,500
4 Lakewood Center Mall, Lakewood, CA 2,390,000
5 Roosevelt Field Mall, Garden City, NY 2,300,000
6 Gurnee Mills, Gurnee, IL 2,200,000
7 The Galleria, Houston, TX 2,100,000
8 Randall Park Mall, North Randall, OH 2,097,416
9 Oakbrook Shopping Center, Oak Brook, IL 2,006,688
10 Sawgrass Mills, Sunrise, FL 2,000,000
10 The Woodlands Mall, The Woodlands, TX 2,000,000
10 Woodfi eld, Schaumburg, IL 2,000,000

Find the mean, median, and mode of the gross leasable areas.

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Problem 22

The table lists the areas of some large shopping malls in the United States.
Mall $\qquad$ Gross Leasable Area $\left(\mathrm{ft}^{2}\right)$
1 Del Amo Fashion Center, Torrance, CA 3,000,000
2 South Coast Plaza/Crystal Court, Costa Mesa, CA 2,918,236
3 Mall of America, Bloomington, MN 2,472,500
4 Lakewood Center Mall, Lakewood, CA 2,390,000
5 Roosevelt Field Mall, Garden City, NY 2,300,000
6 Gurnee Mills, Gurnee, IL 2,200,000
7 The Galleria, Houston, TX 2,100,000
8 Randall Park Mall, North Randall, OH 2,097,416
9 Oakbrook Shopping Center, Oak Brook, IL 2,006,688
10 Sawgrass Mills, Sunrise, FL 2,000,000
10 The Woodlands Mall, The Woodlands, TX 2,000,000
10 Woodfi eld, Schaumburg, IL 2,000,000

You are a realtor who is trying to lease mall space in different areas of the country to a large retailer. Which measure would you talk about if the customer felt that the malls were too large for his store? Explain.

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Problem 23

The table lists the areas of some large shopping malls in the United States.
Mall $\qquad$ Gross Leasable Area $\left(\mathrm{ft}^{2}\right)$
1 Del Amo Fashion Center, Torrance, CA 3,000,000
2 South Coast Plaza/Crystal Court, Costa Mesa, CA 2,918,236
3 Mall of America, Bloomington, MN 2,472,500
4 Lakewood Center Mall, Lakewood, CA 2,390,000
5 Roosevelt Field Mall, Garden City, NY 2,300,000
6 Gurnee Mills, Gurnee, IL 2,200,000
7 The Galleria, Houston, TX 2,100,000
8 Randall Park Mall, North Randall, OH 2,097,416
9 Oakbrook Shopping Center, Oak Brook, IL 2,006,688
10 Sawgrass Mills, Sunrise, FL 2,000,000
10 The Woodlands Mall, The Woodlands, TX 2,000,000
10 Woodfi eld, Schaumburg, IL 2,000,000

Which measure would you talk about if the customer had a large inventory? Explain.

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Problem 24

$$\begin{array}{|c|c|}\hline Score & {Frequency} \\ \hline 90 & {3} \\ \hline 85 & {2} \\ \hline 80 & {3} \\ \hline 75 & {7} \\ \hline 70 & {6} \\ \hline 65 & {4} \\ \hline\end{array}$$
Find the variance and standard deviation of the scores.

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Problem 25

$$\begin{array}{|c|c|}\hline Score & {Frequency} \\ \hline 90 & {3} \\ \hline 85 & {2} \\ \hline 80 & {3} \\ \hline 75 & {7} \\ \hline 70 & {6} \\ \hline 65 & {4} \\ \hline\end{array}$$
What percent of the scores are within one standard deviation of the mean?

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Problem 26

$$\begin{array}{|c|c|}\hline Score & {Frequency} \\ \hline 90 & {3} \\ \hline 85 & {2} \\ \hline 80 & {3} \\ \hline 75 & {7} \\ \hline 70 & {6} \\ \hline 65 & {4} \\ \hline\end{array}$$
What percent of the scores are within two standard deviations of the mean?

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Problem 27

Jackson $\qquad$ Washington $\qquad$ King
170, 165, 140, 188, 195 $\qquad$ 144, 177, 215, 225, 197 $\qquad$ 166, 175, 196, 206, 219

Find the standard deviation of the weights for Jackson High.

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Problem 28

Jackson $\qquad$ Washington $\qquad$ King
170, 165, 140, 188, 195 $\qquad$ 144, 177, 215, 225, 197 $\qquad$ 166, 175, 196, 206, 219

Find the standard deviation of the weights for Washington High.

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Problem 29

Jackson $\qquad$ Washington $\qquad$ King
170, 165, 140, 188, 195 $\qquad$ 144, 177, 215, 225, 197 $\qquad$ 166, 175, 196, 206, 219

Find the standard deviation of the weights for King High.

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Problem 30

Jackson $\qquad$ Washington $\qquad$ King
170, 165, 140, 188, 195 $\qquad$ 144, 177, 215, 225, 197 $\qquad$ 166, 175, 196, 206, 219

Which team had the most variation in weights? How do you think this variation will impact their play?

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Problem 31

Explain why the graphs made from the same data look different.

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Problem 32

Describe a situation where the first graph might be used.

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Problem 33

Describe a situation where the second graph might be used.

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Problem 34

Give a sample set of data with a variance and standard deviation of 0.

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Problem 35

Find a counterexample for the following statement. The standard deviation of a set of data is always less than the variance.

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Problem 36

Consider the two sets of data.
A = {1, 2, 2, 2, 2, 3, 3, 3, 3, 4}, B = {1, 1, 2, 2, 2, 3, 3, 3, 4, 4}
Find the mean, median, variance, and standard deviation of each set of data.

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Problem 37

Consider the two sets of data.
A = {1, 2, 2, 2, 2, 3, 3, 3, 3, 4}, B = {1, 1, 2, 2, 2, 3, 3, 3, 4, 4}
Explain how you can tell which histogram below goes with each data set without counting the frequencies in the sets.

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Problem 38

Identify the term that does not belong with the other three. Explain your reasoning.
mode $\qquad$ variance $\qquad$ mean $\qquad$ median

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Problem 39

Use the information on page 717 to explain what statistics a teacher should tell the class after a test. Include the mean, median, and mode of the given data set and which measure of central tendency you think best represents the test scores and why. How will the measures of central tendency be affected if Mr. Dent adds 5 points to each score?

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Problem 40

What is the mean of the numbers represented by $x+1$, $3 x-2,$ and $2 x-5 ?$
A. $2 x-2$
B. $\frac{6 x-7}{3}$
C. $\frac{x+1}{3}$
D. $x+4$

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Problem 41

A school has two backup generators having probabilities of 0.9 and 0.95, respectively, of operating in case of power outage. Find the probability that at least one backup generator operates during a power outage.
F. 0.855
G. 0.89
H. 0.95
J. 0.995

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Problem 42

Determine whether the events are mutually exclusive or inclusive. Then find the probability.
A card is drawn from a standard deck of cards. What is the probability that it is a 5 or a spade?

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Problem 43

Determine whether the events are mutually exclusive or inclusive. Then find the probability.
A jar of change contains 5 quarters, 8 dimes, 10 nickels, and 19 pennies. If a coin is pulled from the jar at random, what is the probability that it is a nickel or a dime?

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Problem 44

Two cards are drawn from a standard deck of cards. Find each probability.
P(ace, then king) if replacement occurs

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Problem 45

Two cards are drawn from a standard deck of cards. Find each probability.
P(ace, then king) if no replacement occurs

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Problem 46

Two cards are drawn from a standard deck of cards. Find each probability.
P(heart, then club) if no replacement occurs

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Problem 47

Two cards are drawn from a standard deck of cards. Find each probability.
P(heart, then club) if replacement occurs

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Problem 48

The Energy Booster Company keeps their stock of Health Aid liquid in a tank that is a rectangular prism. Its sides measure $x-1$ centimeters, $x+3$ centimeters, and $x-2$ centimeters. Suppose they would like to bottle their Health Aid in $x-3$ containers of the same size. How much liquid in cubic centimeters will remain unbottled?

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Problem 49

Find each percent.
68% of 200

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Problem 50

Find each percent.
68% of 500

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Problem 51

Find each percent.
95% of 400

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Problem 52

Find each percent.
95% of 500

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Problem 53

Find each percent.
99% of 400

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Problem 54

Find each percent.
99% of 500

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