Question

A data set is displayed using a dot plot. The range of the data is between 50 and 90, and the distribution is skewed left. Which measure of center, the mean or median, is probably a better representation of the data? Explain your reasoning.

Answer 1

Apologies for the confusion in my previous response. Given that the distribution is skewed left, the median is likely a better representation of the data's center than the mean.

Skewed left distributions have a longer tail towards the lower values, indicating that there are few extreme values on the left side. These extreme values can have a significant impact on the mean, pulling it towards the left and making it an inaccurate representation of the typical value.

In contrast, the median is less affected by extreme values since it only considers the middle value when the data is sorted. It represents the value that separates the lower 50% of the data from the upper 50%, making it more robust against outliers or extreme values.

Hence, in a skewed left distribution, the median is generally a more reliable measure of the data's center than the mean.