Question

A group counselor decides to make graphs of the psychological test data for all of her clients over the past year. when she plots the distribution of beck depression inventory data, she notices it it skewed to the left. which of the following statements is true if a distribution is skewed to the left?

a. the mean is greater than the median
b. the mean is less than the median
c. the mean and median are the same
d. the mode is the best measure of center

Answer 1

Option b) is correct option. Extreme values on the lower end of the distribution tend to pull the mean down, making it less than the median, which is more centrally located and less affected by those extreme values.

Step-by-step explanation:

If a distribution is skewed to the left, this means that the tail on the left side of the distribution's peak is longer than the right side. In such a distribution, it is typically observed that the mean is less than the median. The reason for this is that the mean, which is the average of all values, is influenced more by the lower (left-side) values in the skew, pulling it further in the direction of the skew than the median, which is the middle value and is not as affected by the extreme values. Therefore, when the group counselor analyses her data from the Beck Depression Inventory and finds that it is skewed to the left, she can deduce that the mean of her data is likely to be lower than the median.

In distributions with skewness, the mode, median, and mean are not the same. The mode often refers to the most frequently occurring value in a dataset and can be less affected by skew. However, when choosing the best measure of center for a skewed distribution, it is generally recommended to use the median as it is not influenced as much by extreme scores. If we consider the correct option for the case of left skewness, it is 'b. the mean is less than the median' which is the statement that holds true.