Statistics for the Behavioral Sciences

Gregory J. Privitera

Chapter 3 Summarizing Data Central Tendency - all with Video Answers

Educators

Chapter Questions

02:39

Problem 1

State the statistical notation for each of the following terms:
a. Population size
b. Sample size
c. Population mean
d. Sample mean

Andy Wong

Numerade Educator

01:43

Problem 2

What is central tendency?

Ryan Mcalister

Numerade Educator

01:43

Problem 3

Which type of central tendency is always located at the center or in the middle of a distribution?

Ryan Mcalister

Numerade Educator

01:00

Problem 4

How do the sample mean and population mean differ?

Harsh Gadhiya

Numerade Educator

01:09

Problem 5

List five characteristics of the mean.

Ryan Mcalister

Numerade Educator

02:30

Problem 6

When is the weighted mean equal to the arithmetic mean for combining the mean for two or more samples?

Evelyn Cunningham

Numerade Educator

01:24

Problem 7

The mode is an appropriate measure for describing what types of data?

Harsh Gadhiya

Numerade Educator

01:55

Problem 8

The median is an appropriate measure for describing what types of data?

Trinity Steen

Numerade Educator

01:55

Problem 9

The mean is an appropriate measure for describing what types of data?

Trinity Steen

Numerade Educator

01:30

Problem 10

What value represents:
a. The midpoint of a distribution? Explain.
b. The balance point of a distribution? Explain.
c. The zero point of a distribution? Explain.

Lucas Finney

Numerade Educator

View

The following frequency distribution table lists the time (in minutes) that participants were late
for an experimental session. Compute the sample mean, median, and mode for these data.
$$
\begin{array}{|l|l|}
\hline \text { Time (min) } & \text { Frequency } \\
\hline 0 & 5 \\
\hline 2 & 2 \\
\hline 6 & 1 \\
\hline 8 & 3 \\
\hline 9 & 2 \\
\hline
\end{array}
$$

Emily Himsel

Numerade Educator

02:05

Problem 12

The following table lists the number of text messages sent per day in a sample of college
students and a sample of their parents.
$$
\begin{array}{|l|l|l|l|}
\hline \multicolumn{2}{|c|}{\text { College Students }} & \multicolumn{2}{c|}{\text { Parents }} \\
\hline 43 & 7 & 24 & 21 \\
\hline 12 & 50 & 0 & 17 \\
\hline 14 & 15 & 20 & 19 \\
\hline 13 & 21 & 21 & 5 \\
\hline 54 & 21 & 3 & 10 \\
\hline
\end{array}
$$
a. Compute the mean, the median, and the mode for the college students' and parents' data.
b. Based on the shape of the distribution for each sample, which measure of central tendency is most appropriate for describing each sample? Explain how describing each sample with only the most appropriate measure might be misleading.

John Long

Numerade Educator

01:01

Problem 13

A researcher records the number of hours (per week) that single mothers spend at work and
states that the data are distributed normally. Which measure of central tendency is most appropriate
for describing these data?

James Kiss

Numerade Educator

01:01

Problem 14

A psychologist records the duration of natural labor (in hours) in a sample of 36 first-pregnancy mothers. Based on the duration data given in the following table, which measure of central tendency is most appropriate for describing these data?
$$
\begin{aligned}
&\begin{array}{|l|l|l|l|}
\hline 1 & 5 & 6 & 2 \\
\hline 7 & 3 & 4 & 7 \\
\hline & & &
\end{array}\\
&\begin{array}{|l|l|l|l|}
\hline 10 & 7 & 5 & 6 \\
\hline 4 & 3 & 2 & 11 \\
\hline 5 & 9 & 8 & 5 \\
\hline 6 & 6 & 9 & 7 \\
\hline 4 & 5 & 6 & 4 \\
\hline 8 & 8 & 10 & 9 \\
\hline 8 & 7 & 6 & 3
\end{array}
\end{aligned}
$$

James Kiss

Numerade Educator

01:11

Problem 15

A researcher records the levels of attraction for various fashion models among college students. He finds that mean levels of attraction are much higher than the median and mode for these data.
a. What is the shape of the distribution for the data described in this study?
b. Which measure of central tendency is most appropriate for describing these data? Explain.

Harsh Gadhiya

Numerade Educator

01:06

Problem 16

A colleague measures the following heights (in inches) of 10 CEOs selected at random: 72,75 , $75,66,64,79,79,75,70$, and 72 . Which measure of central tendency is most appropriate for describing these data? Hint: Draw the shape of this distribution first.

Nick Johnson

Numerade Educator

01:39

Problem 17

A neuroscientist measures the reaction times (in seconds) during an experimental session in a sample of cocaine-addicted $(n=8)$, morphine-addicted $(n=12)$, and heroin-addicted $(n=6)$ rats. Mean reaction times in each sample are 11,18 , and 13 seconds, respectively. What is the weighted mean for all three samples? Hint: The overall mean is not $14.0$ seconds.

Sheryl Ezze

Numerade Educator

01:01

Problem 18

A family counselor records the number of sessions required for children to complete counseling following the loss of a family member. The counselor finds that most boys complete counseling in 12 sessions, whereas most girls require 15 sessions to complete counseling. If the data for boys and girls are combined, what type of distribution best describes the combined data?

James Kiss

Numerade Educator

View

Problem 19

A sports psychologist uses the body mass index (BMI) score to measure health in a sample of 60 athletes and determines that 20 are healthy, 26 are overweight, and 14 are obese. Which measure of central tendency is most appropriate for describing these data?

Rashmi Sinha

Numerade Educator

03:22

Problem 20

A cognitive psychologist was interested in the ability of men and women to multitask-a cognitive skill thought to engage short-term or working memory. The psychologist observed a sample of 5 men $(n=5)$ and 8 women $(n=8)$ and measured the number of tasks they could accurately complete within a short time frame. He found that men completed $2.3$ tasks on average $(M=2.3)$, whereas women completed $4.5$ tasks on average $(M=4.5) .$ What is the weighted mean for both samples? Hint: The overall mean is not $3.4$ tasks.

Shu Naito

Numerade Educator

01:09

Problem 21

Based on the scale of measurement for each variable listed below, which measure of central tendency is most appropriate for describing the data?
a. The distance in miles that a group of athletes run to train for a marathon
b. The rankings of college undergraduate academic programs
c. The blood type (e.g., Type A, B, AB, O) of a group of participants

Kimberly Waterbury

Numerade Educator

03:11

Problem 22

An instructor gives students a surprise quiz and records a mean grade of 12 points. What is the new mean value if the instructor does each of the following?
a. Adds 10 points to each quiz
b. Subtracts 2 points from each quiz
c. Doubles each quiz score
d. Divides each quiz score in half

Moses Obasola

Numerade Educator

01:49

Problem 23

Children participating in a 1-week summer camp made five new friends on average during the first 6 days of camp. If each child made two more friends on the last day of camp, then how many friends on average did the children make during the 1-week summer camp?

Vicki Stebbins

Numerade Educator

03:59

Problem 24

A sample of 26 patients with major depressive disorder (MDD) showed an average of five symptoms of the disorder prior to diagnosis. What is the sum of the differences of scores from the mean in this example?
Based on the example below, answer Questions 25 to 28 :
A group of researchers measures the weight of five participants prior to a clinical weight loss intervention. They record the following weights (in pounds): $200,250,150,100$, and 300 pounds. The mean is 200 pounds.

Pammi Eswari

Numerade Educator

07:20

Problem 25

The researchers realize that the scale was not accurate for the individual weighing 300 pounds, so they reweigh that individual and record 250 pounds. Will the mean increase or decrease in this situation?

Qiao Ruan

Numerade Educator

01:33

Problem 26

Instead, the researchers reweigh the 300 -pound individual and record a new weight of 350 pounds. Will the mean increase or decrease in this situation?

Allison Knapp

Numerade Educator

02:27

Problem 27

Using the original example of five weights, the researchers add a sixth participant to the sample.
a. If the sixth participant weighs 240 pounds, will the mean increase, decrease, or not change?
b. If the sixth participant weighs 200 pounds, will the mean increase, decrease, or not change?
c. If the sixth participant weighs 180 pounds, will the mean increase, decrease, or not change?

Terrisa R

Numerade Educator

00:49

Problem 28

The researchers implement their weight loss intervention with the original five participants and find that each participant loses exactly 10 pounds in the first 3 weeks. Without recalculating the mean, what is the new mean weight?

Brian Austin

Numerade Educator

01:08

Problem 29

General life satisfaction across culture. Gilman and colleagues (2008) measured general life satisfaction in 1,338 adolescents from two individualistic nations (Ireland, United States) and two collectivist nations (China, South Korea) using the Multidimensional Students' Life Satisfaction Scale (MSLSS). Mean participant scores on the MSLSS are given in the following table.
$$
\begin{array}{|l|l|l|}
\hline \multirow{2}{*}{\text { Nation }} & \multicolumn{2}{|c|}{} \\
\cline { 2 - 3 } & \text { Gender } \\
\cline { 2 - 3 } \text { United States } & 4.39 & 4.61 \\
\hline \text { Ireland } & 4.37 & 4.64 \\
\hline \text { China } & 4.41 & 4.56 \\
\hline \text { South Korea } & 3.92 & 3.78 \\
\hline
\end{array}
$$
Mean MSLSS scores by gender and nation in this study.
a. Among which group was general life satisfaction lowest on average?
b. Among which group was general life satisfaction highest on average?

Dominador Tan

Numerade Educator

05:32

Problem 30

Family income in the middle class. Bauer et al. (2011) identified the median income of a middle-class family in their sample to be $\$ 84,200$ annually; the mean family income was $\$ 85,300$ annually. In their data, the lowest family income reported in this group was $\$ 65,100$ annually, and the highest family income reported was $\$ 103,400$ annually. Based on the data given, was the mean an appropriate value to summarize these data? Explain.

Jon Southam

Numerade Educator

07:10

Problem 31

Alcohol abuse and self-esteem. Malcolm (2004) stated that "although heavy [alcohol] drinking was associated with low self-esteem for women [on average]; the opposite was true for men" (p. 41). Based on this citation, was the mean self-esteem score larger for heavy-drinking men or heavydrinking women?

Alex Loukas

Numerade Educator

03:08

Problem 32

Helping smokers quit by race. Patten and colleagues (2008) stated that "among nonsmokers who indicated they were close to a smoker whom they thought should quit, Black [participants] were most often concerned about a family member whereas White [participants] endorsed concern most often for a friend" (p. 496 ). What are the most common concerns (or mode) for each race?

Evelyn Cunningham

Numerade Educator

01:18

Problem 33

The convenience of eating. Privitera and Zuraikat (2014) conducted a study to test whether the proximity of food influences consumption. They placed a bowl of popcorn or apple slices in a container on a table (near) or 2 meters from a participant (far). Do the data in the following figure support their hypothesis that the more proximate the food, the more participants will eat of it? Explain.

Dominador Tan

Numerade Educator

01:14

Problem 34

Social support and stroke-induced aphasia. Hilari and Northcott (2006) used a Social Support Survey (SSS) to gauge how well supported individuals suffering from stroke-induced aphasia (a language disorder) felt more than 1 year following the stroke. They reported that "in terms of social support, the SSS scores were negatively skewed with a mean of $3.69$, suggesting that participants felt overall well supported" (Hilari \& Northcott, 2006, p. 17). Based on their findings, what additional measure of central tendency would be appropriate to report with these data? Explain.

Marc Lauzon

Numerade Educator

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34