Chapter 2.2, Problem 46E

(a)

To determine

Discuss and identify the location of the mean and median by letter.

Answer to Problem 46E

Mean is located at A, and median is located at A.

Explanation of Solution

Given information:

  

The graph to the left of A is the mirror image of the graph to the right of A. Thus, the distribution is symmetric.

For the distribution to be symmetric, it is expected that both the median and the mean lie at the center of the distribution (at point A).

Thus, A represents the mean, and A represents the median also.

(b)

To determine

Discuss and identify the location of median and mean by letter.

Answer to Problem 46E

Mean is located at A, and median is also located at B.

Explanation of Solution

Given information:

  

In the graph, peak of the distribution is to the right, and the distribution is skewed to the left, whereas, a tail of more unusual values is to the left.

As the median is resistant and mean is not resistant, the mean is more influenced by the unusual high values in the left − skewed distribution.

It is expected that neither the median nor the mean lies at the peak of the distribution, because both mean and median are somewhat influenced by unusual high values in the left − skewed distribution such that one measure affects more than the other.

Although, the mean is lower than the median and neither lies at the peak. Thus, A represents the mean, and B represents the median.