Example 2.32 from Statistics, 2.6 Skewness and the Mean, Median, and Mode

Skewness and the Mean, Median, and Mode: example 2.32

Statistics are used to compare and sometimes identify authors. The following lists show 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

Make a dot plot for the three authors and compare the shapes.
Calculate the mean for each.
Calculate the median for each.
Describe any pattern you notice between the shape and the measures of center.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

1
Solution
1. Figure 2.21 Terry’s distribution has a right (positive) skew.
  
  Figure 2.22 Davis’s distribution has a left (negative) skew.
  
  Figure 2.23 Maris’s distribution is symmetrically shaped.
2. Terry’s mean is 3.7, Davis’s mean is 2.7, and Maris’s mean is 4.6.
3. Terry’s median is 3, Davis’s median is 3, and Maris’s median is four. It would be helpful to manually calculate these descriptive statistics, using the given data sets and then compare to the graphs.
4. It appears that the median is always closest to the high point (the mode), while the mean tends to be farther out on the tail. In a symmetrical distribution, the mean and the median are both centrally located close to the high point of the distribution.

How did it go?

Solution

Solution