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Difficulty: EasyMean, Median, and Mode

The scores of a student on five quizzes are 72,85,90,78,72, 85, 90, 78, and 9595. What is the positive difference between the median and the arithmetic mean of these five quiz scores?

Answer: 1

Answer

The positive difference between the median and the arithmetic mean of the five quiz scores is 11.
To find the arithmetic mean, sum all five scores (72+85+90+78+95=42072 + 85 + 90 + 78 + 95 = 420) and divide by 55, yielding 8484. To find the median, list the scores in ascending order (72,78,85,90,9572, 78, 85, 90, 95); the 3rd score is 8585. The positive difference between the median (8585) and the arithmetic mean (8484) is 11.

Step-by-Step Solution

1
Calculate the arithmetic mean of the given set of scores.
The sum of the scores is 72+78+85+90+95=42072 + 78 + 85 + 90 + 95 = 420. Dividing by 5 gives an arithmetic mean of 8484.
The mean is defined as the total sum of all values divided by the number of values.
2
Order the scores in ascending order to identify the median.
The ordered list is 72,78,85,90,9572, 78, 85, 90, 95. The middle term (the 3rd value) is 8585.
The median of a set with an odd number of elements is the middle value when arranged in numerical order.
3
Subtract the arithmetic mean from the median to find the positive difference.
85−84=185 - 84 = 1.
The question asks for the positive difference between the median and the arithmetic mean.

Key Concept

Calculating and comparing the arithmetic mean and median of a finite numerical data set.
Estimated Time:1m 0s
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Topics

Mean, Median, and Mode

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