A histogram of a set of data indicates that the distribution of the data is skewed right. Which measure of central tendency will likely be larger, the mean or the median? Why? Choose the correct answer below. A. The mean will likely be larger because the extreme values in the right tail tend to pull the mean in the direction of the tail. B. The median will likely be larger because the extreme values in the right tail tend to pull the median in the direction of the tail. C. The median will likely be larger because the extreme values in the left tail tend to pull the median in the opposite direction of the tail. D. The mean will likely be larger because the extreme values in the left tail tend to pull the mean in the opposite direction of the tail.

Question

Mathematics

Esperanza Jensen

19 September, 23:50

A histogram of a set of data indicates that the distribution of the data is skewed right. Which measure of central tendency will likely be larger, the mean or the median? Why? Choose the correct answer below. A. The mean will likely be larger because the extreme values in the right tail tend to pull the mean in the direction of the tail. B. The median will likely be larger because the extreme values in the right tail tend to pull the median in the direction of the tail. C. The median will likely be larger because the extreme values in the left tail tend to pull the median in the opposite direction of the tail. D. The mean will likely be larger because the extreme values in the left tail tend to pull the mean in the opposite direction of the tail.

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Answers (1)

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Amani Mathis · Answer 1

The correct option is (A).

Step-by-step explanation:

A distribution is known as to be skewed to the right, or positively skewed, when maximum of the data are collected on the left of the distribution.

A distribution is said to be skewed to the left, or negatively skewed, if maximum of the data are collected on the right of the distribution.

For a right-skewed data, Mean > Median.

When the histogram of a data set is either left - skewed or right-skewed, there are extreme values at the end of the graph, which tends to pull the mean in the direction of the tail of the distribution. If the distribution of the data is right - skewed, there are large observations towards the right tail. These observations tend to increase the value of the mean, while having slight effect on the median.

Thus, the correct option is (A).