variabilityNo variability8 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
Learning Objectives
Understand the properties of the normal curve
Summarize the history of the normal curve and how it relates to current statistical practice
Describe the common uses of the normal curve
Module Summary
The normal curve is a symmetric, bell-shaped curve that has an inflection point (meaning the curve bends) at 1 standard deviation (SD) above and below the mean. The shape of the normal curve is how a distribution with an infinite number of scores would appear. This means that the normal curve is theoretical, as opposed to an actual distribution of scores. However, we can expect that scores will distribute themselves in a manner similar to that of the normal distribution, especially as the size of the sample grows beyond n > 30.
The data sets in this book will rarely fall in a perfect normal curve. However, the properties of the normal curve are robust to distributions that may violate its shape. This indicates that although our data may not look perfectly normal, you can still use the special features of the normal curve to understand our sample.
The benefit of using the normal curve is that you are able to determine the proportion (percentage) of scores that will fall within 1, 2, and 3 SD of the mean. In a normal distribution, you can always expect that about 68% of the scores will fall within ±1 SD of the mean, about 95% of the scores will fall within ±2 SD of the mean, and about 99% of the scores will fall within ±3 SD of the mean. This means that a score that falls 1 SD above the mean will fall in the same place on the normal curve regardless of what is being measured. Aside from knowing the proportion of scores at a specific
