Five boxes of mangoes hold different numbers of fruit, with a median of 18 fruit. A sixth box of 30 mangoes, the largest of all, is added, and the median of the six boxes becomes 20. Among the original five boxes, how many mangoes are in the box that comes 4th when they are arranged from fewest to most?

20Correct answerYour answer22Correct answerYour answer24Correct answerYour answer30Correct answerYour answer

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CorrectNot quiteAnswer B

Correct answer: B

In order, the five boxes are a, b, 18, d, e with d above 18.
The new box of 30 goes at the end, so the six in order are a, b, 18, d, e, 30.
The new median is the average of the 3rd and 4th: $\frac{18 + d}{2} = 20$ , so $d = 22$ .

Worth noting

20 takes the new median as the box itself. 24 averages 18 and 30, as if the new box were in the middle.

Ten questions from Mean, Median and Mode, at your own pace.

Explanation