Question

Which of the following is likely to have a mean that is smaller than the median?

1) Normal distribution
2) Skewed left distribution
3) Skewed right distribution
4) Uniform distribution

Answer 1

A skewed left distribution will typically have a mean that is smaller than the median due to the pull of the lower values on the mean.

Step-by-step explanation:

The distribution likely to have a mean that is smaller than the median is a skewed left distribution. In such a distribution, the long tail is on the left side of the peak, and it pulls the mean toward the lower values, therefore, the mean will usually be smaller than the median. For instance, if we consider a set of numbers like 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, the mean is likely to be smaller than the median due to the greater frequency of lower numbers. Conversely, a normal distribution will have the mean, median, and mode all at the same point, and a uniform distribution has an equal frequency of all numbers, so the mean and median will be very close if not the same.