Chapter 2.1, Problem 31E

(a)

To determine

To find: the points where the mean and the median fall

Answer to Problem 31E

Mean is C, median is B

Explanation of Solution

Given:

  

Calculation:

Mean is C, median is B (the right skew pulls the mean to the right).

  

The distribution is right-skewed (tail of extreme values to the right) andsince the mean is more influenced by extreme values than the median, the mean needs to lie to the right of the median.

The median and the mean both do not lie at A. because they cannot lie on the peak of a skewed distribution (tail of extreme values causes both to lie more to the right). Thus we then know:

B= Median

C= Mean

Conclusion:

Therefore, Mean is C, median is B

(b)

To determine

To find: the points where the mean and the median fall

Answer to Problem 31E

Mean is B, median is also B

Explanation of Solution

Given:

  

Calculation:

  

Since the distribution is symmetric about its middle point B (graph is mirror image to the left of the middle as it is to the right), then the mean lies at this middle point:

  $\mu =B$

Since the area under the graph is also 0.50 to either side of the mean:

  MEDIAN = B

Mean is B, median is also B (this distribution is symmetric).

Conclusion:

Therefore, Mean is B, median is also B