ACT Math · Statistics and data analysis

What is the median of the data set 4, 7, 7, 9, 12, 15, 7, 20?

What is the median of the data set 4, 7, 7, 9, 12, 15, 7, 20?

Answer and explanation

Answer: B: 8

First order the data: 4,7,7,7,9,12,15,204, 7, 7, 7, 9, 12, 15, 20. There are 88 values, so the median is the mean of the 4th and 5th values: 7+92=8\frac{7+9}{2}=8, choice B. Choice A (77) is the mode, the most frequent value. Choice C (99) takes only the 5th value rather than averaging the two middle values. Choice D (10.37510.375) is not the median; the mean of these values is 818≈10.1\frac{81}{8}\approx10.1. The median must be found after sorting; using the original order gives a different, wrong middle.

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