Solution to Exercise 1.37.

  Problem Statement: The article ``Snow Cover and Temperature Relacion-SilipS in North America and Eurasia'' used statistical techniques to relate the amount of snow cover on each continent to average continental temperature. Data presented there included the following ten observations of October snow cover for Eurasia during the years 1970-1979 (in million km²):

$$6.5 \quad 12.0 \quad 14.9 \quad 10.0 \quad 10.7 \quad 7.9 \quad 21.9 \quad 12.5 \quad 14.5 \quad 9.2$$

What would you report as a representative, or typical, value of October snow cover for this period, and what prompted your choice?

Solution: In minitab, I did a dotplot (see description in the book; a sample of size 10 is too small for a histogram). The plot was saved as a *.jpg file (from the File menu, I selected ``Save Plot as ...''). This is shown below.

The descriptive statistics were computed in minitab (Stat menu $\rightarrow$ Basic Statistics $\rightarrow$ Display Descriptive Statistics) and are given below (I used the ``Save Session Window as ...'' selection from the file menu):

Worksheet size: 5000 cells
Macro is running ... please wait

Descriptive Statistics


Variable             N       Mean     Median     TrMean      StDev    SE Mean
snowcove            10      12.01      11.35      11.46       4.39       1.39

Variable       Minimum    Maximum         Q1         Q3
snowcove          6.50      21.90       8.88      14.60

Because of the outlier, I would say the Median of 11.35 or Trimmed Mean of 11.46 (which are almost the same) would be a better representative value than the mean of 12.01. My preference is the Median as it is more widely used and easier to explain.