The following histogram displays data taken from a random sample of instrumentalists from a music conservatory who revealed their average daily practice duration (in hours). Which of the following statements is the most accurate interpretation of the data?
A. the mean number of hours of practice is less than the median number of hours of practice
B. the mean number of hours of practice exceeds the median number of hours of practice
C. the median number of hours of practice is exactly 5 hours
D. the mean number of hours of practice is exactly 5 hours
When the median equals the mean, the graph will look symmetric (it is a bell-shaped curve or a symmetric histogram with equal fall to the right and left of the mean). In this example, there is no symmetry, thus the median cannot equal the mean. The median point divides the area in half (the two areas on both sides of the median point must be equal). The graph appears to be skewed to the right (it gets thinner to the right and builds up to the left). Thus the median number of hours of practice should be less than the mean number of hours of practice.
Let's check this result: there are 20 + 35 + 25 + 10 + 5 = 95 instrumentalists in total, so that the median number of hours of practice will fall on the 48th lowest number of hours of practice (the middle number of students is 48 out of 95, calculated as 95/2 = 47.5, which is rounded to 48). Since 20 students practice 0-2 hours daily, we see 2-4 hours of practice from the 21st to 55th student. This is where the median (48) will fall, so that the median number of hours of practice is in the 2-4 hours range.
Since there are outliers (values that are extreme to the right of the median), the mean will exceed the median. Thus the correct answer choice is (B).
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