Question value-
| Value | Frequency |
| 1 | a |
| 2 | 2a |
| 3 | 3a |
| 4 | 2a |
| 5 | a |
The frequency distribution above summarizes a set of data, where a is a positive integer. How much greater is the mean of the set of data than the median?
0
1
2
3
Value Frequency 1 a 2 2 a 3 3 a 4 2 a 5 a The
Hard-difficulty · SAT Math · One-Variable Data & Statistics — Mean, median, mode, range. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.
Answer explanation
Choice A is correct. Since the frequencies of values less than the middle value, 3, are the same as the frequencies of the values greater than 3, the set of data has a symmetric distribution. When a set of data has a symmetric distribution, the mean and median values are equal. Therefore, the mean is 0 greater than the median.
Choices B, C, and D are incorrect and may result from misinterpreting the set of data.
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