Which two measures of central tendency are equal in a perfectly symmetric distribution?

Which two measures of central tendency are equal in a perfectly symmetric distribution?

• A. Mean and Median
• B. Mean and Mode
• C. Median and Mode
• D. All three

Answer: (A)

In a perfectly symmetric distribution, the data balance around a central point. The mean is the balance point of all values, while the median is the value that divides the data into two equal halves. Because the left and right sides mirror each other, the center where the data balance also sits at the middle value. Therefore, the mean and the median coincide. If the distribution is also unimodal, the mode will align with them too, but the essential point is that symmetry makes the mean equal to the median. In skewed distributions, this equality generally does not hold because the tail pulls the mean away from the median.

In a perfectly symmetric distribution, the data balance around a central point. The mean is the balance point of all values, while the median is the value that divides the data into two equal halves. Because the left and right sides mirror each other, the center where the data balance also sits at the middle value. Therefore, the mean and the median coincide. If the distribution is also unimodal, the mode will align with them too, but the essential point is that symmetry makes the mean equal to the median. In skewed distributions, this equality generally does not hold because the tail pulls the mean away from the median.