Find the standard deviation

d. 7.3

Step-by-step explanation:

To get the standard deviation of a population of data, first take the sum of all the values, and divide it by the count to get the mean (average).

75 [1] + 90 [2] + 75 [3] + 80 [4] + 90 [5] + 80 [6] + 100 [7] + 85 [8] + 80 [9] + 85 [10] = 840.

Then divide by the count which is 10.

840/10 = 84 [This is the mean of the data.]

Then subtract every point of data from the mean and square it:

(75-84)^2 + (90-84)^2 + (75-84)^2 + (80-84)^2 + (90-84)^2 + (80-84)^2 + (100-84)^2 + (85-84)^2 + (80-84)^2 + (85-84)^2 = 81 + 36 + 81 + 16 + 36 + 16 + 256 + 1 + 16 + 1 = 540.

Then to get the variance, divide this all by the count.

540/10 = 54 [This is the variance of the data.]

Then all you have to do to get the standard deviation is take the square root of the variance.

√54 = 3√6 ≈ 7.3 [This is the standard deviation of the data.]