# How big are the distances between scores?

## Assignment: Measures of Central Tendency and Variability

Last week, you learned how to summarize a distribution by using frequency distribution tables and various graphs. The shape the frequency distribution forms is important, but frequency tables and graphs are not always the most efficient or meaningful way to summarize large amounts of data. In addition to graphing the shape of the distribution, statistics can be computed to provide even more information about the scores. Measures of central tendency tell us how the scores in the data set “hang together.” What score or scores are “typical” for the data set? Measures of variability help us understand how scores are spread out. How big are the distances between scores? Computing measures of central tendency, such as the mean, median, and mode, and measures of variability, such as the range and standard deviation, is often the first step researchers take after collecting data for a study.

This application will allow you to practice computing and interpreting some common measures of central tendency and measures of variability, both by hand and with the statistical software package SPSS. Download the data set that you will use for this assignment from the Weekly Data Set forum. Be sure to watch this week’s instructional video in the introduction or Learning Resources folder before beginning your Application Assignment.

Scenario: Imagine that your employer is hosting a walking competition. Employees are to report the number of minutes they walk each week. Your employer has asked you to compute descriptive statistics on the data from the first week of the competition to help him know how much people are walking.

You can find the data for this Assignment in the Weekly Data Set forum.

To complete this Assignment, submit by Day 7 calculations of the following measures of central tendency and measures of variability by hand:

##### By Day 7

To complete this Assignment, submit calculations of the following measures of central tendency and measures of variability by hand:

1. Mean
2. Median
3. Mode
4. Range
5. Deviation of the highest score from the mean
6. Estimated population standard deviation
7. X2 (explain your calculations, but you do not to interpret this result in relation to the scenario)
8. (∑X)2 (explain your calculations, but you do not to interpret this result in relation to the scenario)

For each measure you compute by hand, include an explanation of:

• Your calculations (explain the steps)
• What that measure tells you about the number of minutes walked by employees

For example, each of your answers might look something like this: “The mean of this sample is ______ minutes walked in the first week. The mean is calculated by _________________. The mean tells me that participants in the sample walked ____________ in the first week.”

1. Compute the mean and standard deviation in SPSS. Note: Your hand-calculated mean and standard deviation may differ somewhat from the calculations in SPSS due to rounding.
2. Describe how the standard deviation (SD) and the deviation of a single score from the mean differ in the information they provide.
3. Without redoing any calculations, think critically about how each measure would be affected if the lowest score was eliminated from the data set. Explain if each measure (mean, median, mode, deviation of the highest score from the mean, and standard deviation) would increase, decrease, or stay the same.
4. Identify the type of distribution (positive skew, negative skew, or normal distribution) the data create. Explain how you know the type of distribution and what it tells you about the sample. 