"If a group of 12 boys with different heights: 5′;5′2′′;5′4′′;5′6′′;5′8′′;5′10′′;6′;6′2′′;6′4′′;6′6′′;6′8′′;6′10′′ , which of the following is correct? A) No boy in the group represents the median height of the group. B) There is a boy in the group who represents the arithmetic mean (average) height of the group. C) The sum of the number of boys with less than the median height and the number of boys with greater than the median height is equal to 11. D) The arithmetic mean (average) height is greater than the median height of the group."

Question

"If a group of 12 boys with different heights: 5′;5′2′′;5′4′′;5′6′′;5′8′′;5′10′′;6′;6′2′′;6′4′′;6′6′′;6′8′′;6′10′′ , which of the following is correct?   A)	No boy in the group represents the median height of the group. B)	There is a boy in the group who represents the arithmetic mean (average) height of the group. C)	The sum of the number of boys with less than the median height and the number of boys with greater than the median height is equal to 11. D)	The arithmetic mean (average) height is greater than the median height of the group."

Bytelearn · Accepted Answer

Calculate Median Height:  Step 1: Calculate the median height of the group. Since there are 12 boys, the median will be the average of the heights of the 6th and 7th tallest boys. 6th tallest: 5′10′′ 7th tallest: 6′ Median = (5′10′′ + 6′) / 2 Median = (70 inches + 72 inches) / 2 Median = 142 inches / 2 Median = 71 inches or 5′11′′Calculate Mean Height:  Step 2: Calculate the arithmetic mean (average) height of the group. Sum of heights = 5′ + 5′2′′ + 5′4′′ + 5′6′′ + 5′8′′ + 5′10′′ + 6′ + 6′2′′ + 6′4′′ + 6′6′′ + 6′8′′ + 6′10′′ Convert all to inches: 60 + 62 + 64 + 66 + 68 + 70 + 72 + 74 + 76 + 78 + 80 + 82 = 852 inches Average = 852 inches / 12 Average = 71 inches or 5′11′′Check Each Statement:  Step 3: Check each statement. A) Incorrect. The median height is 5′11′′, and there is no boy exactly at 5′11′′. B) Incorrect. The average height is 5′11′′, and there is no boy exactly at 5′11′′. C) Incorrect. There are 6 boys below and 6 boys above the median height, summing to 12, not 11. D) Incorrect. The arithmetic mean and the median are equal, both are 5′11′′.

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