Chapter 1.3, Problem 122E

(a)

To determine

To Explain: the summary statistics on the basis of centre of variability and the resistant.

Answer to Problem 122E

Measure of centre

Resistant

Explanation of Solution

Given:

  $\frac{Q_1+Q_3}{2}$

(I) the average of the first and third quartile is $\frac{Q_1+Q_3}{2}$ for the symmetric distribution, this variable will be equal to the median, the reason is that the symmetric distribution lies exactly in the mid between the first and third quartile. Although the median is a measure of centre, the variable $\frac{Q_1+Q_3}{2}$ is also a measure of centre.

(ii) $Q_1$ And $Q_3$ are resistant to outliers and therefore the variable $\frac{Q_1+Q_3}{2}$ would also be resistant to outliers.

(b)

To determine

To Explain: the summary statistics on the basis of centre of variability and the resistant.

Answer to Problem 122E

Measure of spread

Not resistant

Explanation of Solution

Given:

  $\frac{Max-Min}{2}$

(I) the range is the difference between the maximum and minimum therefore $\frac{Max-Min}{2}$ Although the range is measure of spread, the variable $\frac{Max-Min}{2}$ is also a measure of spread.

(ii) The range is not resisters to outliers and thus the variable $\frac{Max-Min}{2}$ would also not be resistant to outliers.