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Chapter 1: Q37E (page 35)

The article 鈥淪now Cover and Temperature Relationships in North America and Eurasia鈥� (J. Climate and Applied Meteorology, 1983: 460鈥�469) 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 on October snow cover for Eurasia during the years 1970鈥�1979 (in million\({\bf{k}}{{\bf{m}}^{\bf{2}}}\)):

6.5 12.0 14.9 10.0 10.7 7.9 21.9 12.5 14.5 9.2

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

Short Answer

Expert verified

The typical value is mean of the data which is 11.46million \(k{m^2}\).

Step by step solution

01

Given information

The observations on the amount of snow cover for Eurasia during the years 1970-1979 is provided.

02

Compute the typical value

Let x represents the amount of snow cover for Eurasia.

The representative or the typical value is 10% trimmed mean.

10% of 10 data points is equivalent to 1.

The data after removing the smallest and largest observation is as follows,

7.9

9.2

10

10.7

12

12.5

14.5

14.9

The 10% trimmed mean is computed as,

\(\begin{array}{c}\bar x &=& \frac{{\sum {{x_i}} }}{n}\\ &=& \frac{{7.9 + 9.2 + 10 + ... + 14.9}}{8}\\ &=& 11.46\end{array}\)

Thus, the trimmed mean is 11.46.

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