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StatisticsDescriptive Statistics

Positive vs Negative Skew: Letter-Count Dot Plots and Centers

Plot the exact letter counts for three authors, compute each mean and median, and compare right and left tails without assuming symmetry.

Question

Statistics are used to compare and sometimes identify authors. The following lists shows a simple random sample that compares the letter counts for three authors.

Terry: 7; 9; 3; 3; 3; 4; 1; 3; 2; 2 Davis: 3; 3; 3; 4; 1; 4; 3; 2; 3; 1 Maris: 2; 3; 4; 4; 4; 6; 6; 6; 8; 3

a. Make a dot plot for the three authors and compare the shapes.

b. Calculate the mean for each.

c. Calculate the median for each.

d. Describe any pattern you notice between the shape and the measures of center.

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Evidence boundary

This answer uses all three data lists and all four parts of Example 2.31 in the 2013 OpenStax PDF. The dot plots are reconstructed from the exact supplied observations. Maris is not exactly symmetric despite the source solution’s description; no data are changed to fit that claim. Mean–median ordering is not treated as a universal skewness test.