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Chapter 2: Q 45. (page 139)

Mean and median The figure displays two density curves that model

different distributions of quantitative data. Identify the location of the mean and median by letter for each graph. Justify your answers.

Short Answer

Expert verified

Part (a) Mean is located at Cand median is located at B

Part (b) Mean is located at Band the median is also located at B

Step by step solution

01

Part (a) Step 1: Given information

02

Part (a) Step 2: Concept

Neither of these transformations changes the shape of the distribution.

03

Part (a) Step 3: Explanation

The distribution's apex is to the left, and the distribution is skewed to the right, with a tail of more odd values to the right in the graph.

Because the median is resistant while the mean is not, the mean is more influenced by the right-skewed distribution's extremely high values.

Because both the mean and the median are influenced by unusually high values in the right-skewed distribution, one measure impacts more than the other, neither the median nor the mean is predicted to reside at the distribution's peak.

Despite the fact that the mean is higher than the median, neither is at the apex.

As a result, C denotes the mean and B denotes the median.

04

Part (b) Step 1: Given information

05

Part (b) Step 2: Explanation

The graph on B's left is the mirror image of the graph to B's right. The distribution is thus symmetric.

Both the median and the mean should be at the centre of the distribution for the distribution to be symmetric (at point B).

As a result, B stands for both the mean and the median.

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