Standard deviation

Question

Find the mean and standard deviation for the set of data

{25,16,28,6,30,7,26,20,22}

A. Mean: 20; standard deviation: 8.47

B. Mean: 22; standard deviation: 8.47

C. Mean: 20; standard deviation: 8.23

D. Mean: 22; standard deviation: 8.23

Answer 1

Question: Find the mean and standard deviation for the set of data

{25,16,28,6,30,7,26,20,22}

Answer: Let's break up this problem into parts.

FIRST. Find the mean of this data. So do this: 25 + 16 + 28 + 6 + 30 + 7 + 26 + 20 + 22. After that, divide that sum by the number of data points, so 9 in this case. We have (180) ÷ 9 = 20. The mean of this data is 20. (Get rid of options B and D.)

SECOND. Take each data point, subtract the mean, and multiply each difference by itself (that is, square each difference). The order of the data doesn't matter.

(25 - 20)² = (5)² = 25

(16 - 20)² = (-4)² = 16

(28 - 20)² = (8)² = 64

(6 - 20)² = (-14)² = 196

(30 - 20)² = (10)² = 100

(7 - 20)² = (-13)² = 169

(26 - 20)² = (6)² = 36

(20 - 20)² = (0)² = 0

(22 - 20)² = (2)² = 4

THIRD. Add up the numbers we just found.

So do this: 25 + 16 + 64 + 196 + 100 + 169 + 36 + 0 + 4. The sum is 610.

FOURTH. How many data points are in the set? There are nine. Keep that in mind.

(N.B. Students of statistics ought to know that I am working under the assumption that the data provided is population data, which is why I ask for the data set count only. Using the data set count minus 1 assuming that the data were sample data does not get an answer in accordance with the proposed choices.)

FIFTH. Take the number from the third part and divide it by the number from the fourth part.

What is 610 ÷ 9? It is approximately 67.7777. This number is called the variance of the data set, but we need one more step to get the standard deviation of the set.

SIXTH. Take the square root of the number from the fifth step; that is, take the square root of the variance. What is the square root of 67.7777? It is approximately 8.2327, or about 8.23.

Choice C (Mean: 20; standard deviation: 8.23) is correct.