Question

number of months 80 60 40 20 0 -25 -20 -15 -10 -5 0 5 10 15 monthly percent return on common stocks mean < median mean > median mean = median

Explanation:

Step1: Analyze the Distribution Shape

The histogram shows a left - skewed (negatively skewed) distribution? Wait, no, wait. Wait, the left tail (negative returns with small frequencies) and the main body. Wait, actually, the left tail has some small bars (for - 25, - 20, - 15 etc.), but the peak is around 0. Wait, no, let's recall skewness. In a left - skewed (negative skew) distribution, the mean is pulled in the direction of the tail. Wait, no: for a left - skewed distribution, the tail is on the left (lower values). The mean is affected by extreme values. If there are extreme low values (left tail), the mean will be less than the median. Wait, let's think again. The formula for skewness: if the distribution is left - skewed (negative skew), mean < median < mode. If it's right - skewed (positive skew), mode < median < mean.

Looking at the histogram, the left tail (values like - 25, - 20, - 15) has some observations (even though small). These are extreme low values. So the mean will be pulled down (towards the left tail) compared to the median. So in a left - skewed distribution, mean < median.

Step2: Relate to Mean and Median

Since the distribution has a left tail (extreme low values), the mean is less than the median. So the correct relationship is Mean < Median.

Answer:

Mean < Median (the option "Mean < Median")