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.

Data set

Number of Minutes Walked 112 90 100 114 100 146 100 78 122 132 122 94 35 110 122 103 122 100 122 102

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 need to interpret this result in relation to the scenario)
8. (∑X)2 (explain your calculations, but you do not need 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.