Student Study Guide to Accompany Statistics Alive!. Wendy J. Steinberg
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person would be considered an outlier because he or she falls so far away from the mean.
9 The range would not be affected at all by adding scores to the center of the distribution. However, the variance and standard deviation would become smaller.
10 This means that the values all fall on the same scale. The standard deviation is on the scale of the normal curve, which has unique properties that we will encounter in later modules.
11 The standard deviation represents the standardized average deviation that is applicable to the normal curve. The mean absolute deviation uses the absolute value of the deviation scores.
12 The mean absolute deviation does not fall within known places on the normal curve, which is extremely useful in the practice of statistics. Because of this, the mean absolute deviation is not commonly used.
Multiple-Choice Questions
The coach of a basketball team is interested in assessing how well his team shoots free throws. Here is the number of successful free throws that each member of his team made during their last practice session. Use this information for Questions 1 to 5.
1 The coach is asked to provide a quick measure of the dispersion for his team’s free throws. What is the range for his team?011112
2 The coach has more time on his hands and determines the variance. What is it?11.29 (using N), 12.32 (using n − 1)15.52 (using N), 16.92 (using n − 1)18.45 (using N), 13.21 (using n − 1)4.18 (using N), 4.56 (using n − 1)
3 The coach realizes that the variance is difficult to interpret and now wants to know the standard deviation for his team. What is the team’s standard deviation?5.09 (using N), 5.32 (using n − 1)1.18 (using N), 1.23 (using n − 1)4.29 (using N), (using n − 1)3.94 (using N), 4.11 (using n − 1)
4 Shortly after obtaining these data, a new player is added to the team, who makes 10 free throws. If you were to incorporate this new player’s score, which measure of dispersion would not be affected?VarianceStandard deviationRangeMean
5 The coach is interested in using the data from his team to learn about the number of free throws made by all of the teams in the league. This is an example ofdescriptive statistics.inferential statistics.central tendency.dispersion.
6 A distribution of scores is discovered to be highly leptokurtic. How much dispersion would you expect?A small amount because many scores are close to the meanA large amount because many scores are close to the meanA small amount because many scores are distant from the meanA large amount because many scores are distant from the mean
7 How much dispersion can you expect with a constant?A great deal of variabilityA moderate amount of variabilityMinimal variabilityNo variability
8 You want to find the standard deviation for a set of scores to infer the results to a larger group of scores. Which formula should you use?
Here are the responses of 10 individuals on a survey assessing satisfaction at the local Department of Motor Vehicles (DMV; scale is 1–10). Use this information for Questions 9 to 14.
9. What is the range of these ratings?1765
10. What is the variance of these ratings?6.78 (using N), 7.40 (using n − 1)5.09 (using N), 5.55 (using n − 1)7.89 (using N), 8.60 (using n − 1)4.21 (using N), 4.59 (using n − 1)
11. What is the standard deviation of these ratings?2.26 (using N), 2.38 (using n − 1)3.47 (using N), 3.62 (using n − 1)5.70 (using N), 5.95 (using n − 1)6.87 (using N), 7.18 (using n − 1)
12. What is the mean absolute deviation of these ratings?2.083.402.274.58
13. How many scores are more than 1 SD away from the mean?1234
14. What would the standard deviation be if the supervisor of the DMV wanted to make an estimate about the satisfaction of those who have used the DMV?2.381.521.17.5
15. Late one night, Javier is working on some marketing data that are symmetrically distributed. He is very tired and accidentally uses the median instead of the mean when calculating his deviation scores. How will this affect his standard deviation?It will increase it.It will decrease it.It will not affect it.You need more information.
16. You are interested in studying the eye color of your fellow classmates. You obtain the following data: blue, blue, brown, brown, brown, brown, green, green, gray. What would the standard deviation be for this distribution?123You can’t calculate a standard deviation for nominal data.
Jessica is tracking how many glasses of water she drinks each day. Use this information for Questions 17 to 19.
4, 3, 7, 8, 2
17. What is the variance of the number of glasses she drank?48.85 (using N), 60.56 (using n – 1)5.36 (using N), 6.70 (using n – 1)7.45 (using N), 9.31 (using n – 1)6.89 (using N), 8.61 (using n – 1)
18. What is the standard deviation of the number of glasses of water she drank?2.32 (using N), 2.59 (using n – 1)3.45 (using N), 3.86 (using n – 1)6.82 (using N), 7.62 (using n – 1)7.41 (using N), 8.28 (using n – 1)
19. On how many days did Jessica drink a number of glasses within 1 SD of the mean?1234
Multiple-Choice Answers
1 C
2 B
3 D
4 C
5 B
6 A
7 D
8 D
9 C
10 B
11 A
12 A
13 D
14 A
15 C
16 D
17 B
18 A
19 C
Module Quiz
1 The average amount of time people spend on a certain mobile application is 4.5 min/day, and the standard deviation is 0.75. What is the variance of the minutes spent per day on this application?
2 Why do we use n – 1 in the denominator of the variance formula when estimating a population variance from a sample?
3 In general, how would adding outliers to a distribution affect the dispersion?
4 What are descriptive statistics? Give examples of this type of statistic.
5 What are inferential statistics? Why are they important in our study of statistics?
Quiz Answers
1 The variance is 0.56.
2 n – 1 is used in the denominator to correct for a sample’s underestimation of the variability in a population.
3 It would increase the dispersion.
4 Descriptive statistics are those that summarize the data in a sample. Examples of this type of statistic are measures of central tendency and dispersion.
5 Inferential statistics are used to make estimates about a population from a sample. They are important because it can be very difficult to directly measure a population.
Module 7 Percent Area and the Normal Curve
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