# Methods of Research – Descriptive Statistics Assignment

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Methods of Research – Descriptive Statistics Assignment

1. Given the following set of numbers:

2, 4, 4.5, 6, 7.3, 7.9, 9, 10

a. Calculate the mean: 6.34

b. Calculate the median: 6.65

c. Calculate the variance: 6.45

d. Calculate the standard deviation: 2.54

2. Now, add one number to the set, 30, so that we have the following set:

2, 4, 4.5, 6, 7.3, 7.9, 9, 10, 30

a. Calculate the mean and variance of the updated set: Mean: 8.97, Variance: 61.04

b. Compare the means and variances of the set from Questions 1 and 2; which set’s descriptive statistics do you think represent the set of numbers best? Why?

The first set, because the substantial size of the outlier number skewed the data to the right.

3. Take a look at the following table, which presents statistics on the public’s support for tax cuts (higher == more support), divided between Democrats and Republicans. The measure is a basic 7-point scale question, with 1 indicating no support for tax cuts and 7 indicating complete support for tax cuts.

 Mean Standard Deviation Democrats 3.5 1.5 Republicans 5.3 0.3

a. Explain, in plain English, the statistics for each party, being sure to compare the stats from Democrats and Republicans.

b. What does the standard deviation tell us about each party’s tendency to support (or not support) tax cuts?

According to the standard deviation Republicans are more likely to support tax cuts than Democrats.

c. Can we be absolutely certain that the mean of one of the parties shown here is higher/lower than the other, given these statistics? Explain why or why not.

Yes, because we are given the standard deviation.

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