Читать книгу Student Study Guide to Accompany Statistics Alive! - Wendy J. Steinberg - Страница 30

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