# standard deviation

4. 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.

mean Correct: Your answer is correct. min

median Correct: Your answer is correct. min

mode 0 Incorrect: Your answer is incorrect. min

Time (min) Frequency

0 3

5 2

6 5

7 1

9 2

______________________________________________________________________________

7. A neuroscientist measures the reaction times (in seconds) during an experimental session in a sample of cocaine-addicted

(n = 8),

morphine-addicted

(n = 6),

and heroin-addicted rats

(n = 12).

Mean reaction times in each sample were 16, 14, and 12 seconds, respectively. What is the weighted mean for all three samples? Hint: The overall mean is not 14.0 seconds. (Round your answer to two decimal places.)

____________ sec

______________________________________________________________________________

9. A group of researchers measure the weight of five participants prior to a clinical weight loss intervention. They record the following weights (in pounds): 160, 110, 210, 310, and 260 pounds. The mean is 210 pounds.

Using the original example of five weights, the researchers added a sixth participant to the sample.

(a) If the sixth participant weighed 220 pounds, will the mean increase, decrease, or not change?

The mean will increase.

The mean will decrease.

The mean will not change.

(b) If the sixth participant weighed 210 pounds, will the mean increase, decrease, or not change?

The mean will increase.

The mean will decrease.

The mean will not change.

(c) If the sixth participant weighted 180 pounds, will the mean increase, decrease, or not change?

The mean will increase.

The mean will decrease.

The mean will not change.

______________________________________________________________________________

10. 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.

Nation Gender Men Women

United States 4.39 4.61

Ireland 4.37 4.64

China 4.41 4.56

South Korea 3.92 3.78

(a) Among which group was general life satisfaction lowest on average?

women from South Korea

men from the United States

women from Ireland

men from South Korea

women from the United States

men from China men from Ireland

women from China

(b) Among which group was general life satisfaction highest on average?

women from South Korea

men from Ireland

men from South Korea

men from the United States

women from China

women from Ireland

women from the United States

men from China

______________________________________________________________________________

11. What are the degrees of freedom for sample variance?

n − 2

n + 1

n − 1

n

______________________________________________________________________________

12. Based on the empirical rule, what percentage of data fall within 1 SD, 2 SD, and 3 SD of the mean for data that are distributed normally? (Enter your answers to one decimal place.)

% of all scores lie within 1 SD of the mean

% of all scores lie within 2 SD of the mean

% of all scores lie within 3 SD of the mean

______________________________________________________________________________

13. A social scientist measures the number of minutes (per day) that a small hypothetical population of college students spends online.

Student Score Student Score

A 64 F 84

B 86 G 97

C 27 H 92

D 91 I 78

E 92 J 86

(a) What is the range of data in this population?

____________min

(b) What is the IQR of data in this population?

____________min

(c) What is the SIQR of data in this population?

_____________min

(d) What is the population variance?

(e) What is the population standard deviation? (Round your answer to two decimal places.)

_____________min

______________________________________________________________________________

14. A sociologist records the annual household income (in thousands of dollars) among a sample of families living in a high-crime neighborhood. Locate the lower, median, and upper quartiles for the times listed below. Hint: First arrange the data in numerical order.

lower quartile _________ thousand dollars

median _________ thousand dollars

upper quartile __________ thousand dollars

22 36

46 53

38 49

47 31

20 38

______________________________________________________________________________

15. A psychopathologist records the number of criminal offenses among teenage drug users in a nationwide sample of 1,301 participants. To measure the variance of criminal offenses, he computes SS = 46,800 for this sample.

(a) What are the degrees of freedom for variance? ______________________

(b) Compute the variance and standard deviation.

variance ______________

standard deviation ______________

______________________________________________________________________________

16. State whether each of the following will increase, decrease, or have no effect on the population variance.

(a) the sum of squares (SS) increases

This change will increase the population variance.

This change will decrease the population variance.

This change will have no effect on the population variance.

(b) the sample size decreases

This change will increase the population variance.

This change will decrease the population variance.

This change will have no effect on the population variance.

(c) the size of the population increases

This change will increase the population variance.

This change will decrease the population variance.

This change will have no effect on the population variance.

______________________________________________________________________________

17. A researcher measures the time (in seconds) it takes a sample of five participants to complete a memory task. It took four of the participants 1, 2, 2, and 3 seconds. If M = 2, then what must be the fifth time recorded?

______________sec

______________________________________________________________________________

18, An expert reviews a sample of 10 scientific articles (n = 10) and records the following number of errors in each article: 3, 5, 4, 6, 9, 0, 1, 9, 0, and 8. Compute SS, variance, and standard deviation for this sample using the definitional and computational formula. (Round your answers to two decimal places.)

SS ________________________

variance ________________________

standard deviation _____________________ errors

______________________________________________________________________________

19. A professor records the time (in minutes) that it takes 16 students to complete an exam. Compute the SS, the variance, and the standard deviation assuming the 16 students constitute a population and assuming the 16 students constitute a sample. (Round your answers for variance and standard deviation to two decimal places.)

31 39 42 28

43 51 41 20

36 22 19 42

13 40 24 49

(a) the 16 students constitute a population

SS ______________________

variance ____________________

___________________min

(b) the 16 students constitute a sample

SS ___________________

variance _____________________

standard deviation ___________________min

______________________________________________________________________________

20. To study bonding between mothers and infants, a researcher places each mother and her infant in a playroom and has the mother leave for 10 minutes. The researcher records crying time in the sample of infants during this time that the mother was not present and finds that crying time is normally distributed with M = 8 and SD = 1.1.

Based on the empirical rule, state the range of crying times within 68% of infants cried, 95% of infants cried, and 99.7% of infants cried.

(a) 68% of infants cried

______________ to _____________ min

(b) 95% of infants cried

______________ to ______________ min

(c) 99.7% of infants cried

______________