Question

Mr. Viviano would like to report to the principal the smaller measure of center between the mean and the median for the distribution of test scores of his AP Calculus class.

The test scores are as follows: 60, 65, 70, 75, 80, 80, 85, 85, 90, 95, 100.

Answer 1

Value of median is 80 and mean is 80.45. Therefore, the median is gives a smaller measure of center.

Explanation:

We are given some test scores, and we have to report the smaller measure of center between Mean and Median. For this, first we need to calculate these two values.

Median:

Median is the middle value when data is arranged in the ascending order. The given data is already arranged in ascending order and there are 11 numbers in total. So the middle value will be at position:

`(n+1)/(2)`

where n represents the total numbers, which is 11. So for given case, the median will be at:

`(11+1)/(2)=6`

Median will be at 6th position. The number occupying the 6th position is 80.

60, 65, 70, 75, 80, 80, 85, 85, 90, 95, 100.

Therefore, the median is 80.

Mean:

Mean is defined as the sum of values divided by total number of values.

Sum of values = 885

Number of values = 11

So,

Mean of given data =
`(885)/(11) = 80.45`

Value of median is 80 and mean is 80.45. Therefore, the median is gives a smaller measure of center.