In a left-skewed distribution, which statement is true about the relative positions of mean, median, and mode?

In a left-skewed distribution, which statement is true about the relative positions of mean, median, and mode?

• A. The mean is the largest statistic
• B. The mode is the smallest statistic
• C. The mean is the smallest statistic, while the mode is the largest
• D. The median is always the smallest statistic

Answer: (C)

In a left-skewed distribution, the tail extends to the left with some unusually small values. Those small values pull the mean downward, so it sits to the left of the others. The mode is the value that occurs most frequently and, in a left-skewed shape where most data cluster toward higher values, the peak tends to be toward the right, making the mode the largest of the three. The median falls between these two because it splits the data into two halves.

So the usual order is mean is the smallest, median in the middle, and mode the largest. The statement that the mean is the smallest while the mode is the largest directly reflects this pattern.