# Find the range and standard deviation of the set of data.?

Find the range and standard deviation of the set of data.

5, 7, 5, 7, 7, 8, 10

The range is

### 2 Answers

- KrishnamurthyLv 74 months ago
Find the range and standard deviation of the set of data.

5, 7, 5, 7, 7, 8, 10

The range is 5.

The standard deviation is 1.603567451.

- 4 months ago
Sort the data from least to greatest

5 , 5 , 7 , 7 , 7 , 8 , 10

The range is the difference between the least and greatest term

10 - 5 = 5

Find the mean

(5 + 5 + 7 + 7 + 7 + 8 + 10) / 7 =>

(10 + 21 + 18) / 7 =>

(28 + 21) / 7 =>

49 / 7 =>

7

Sum the square of the differences between the mean and each value in the set

(7 - 5)^2 + (7 - 5)^2 + (7 - 7)^2 + (7 - 7)^2 + (7 - 7)^2 + (7 - 8)^2 + (7 - 10)^2 =>

2 * (7 - 5)^2 + 3 * (7 - 7)^2 + (7 - 8)^2 + (7 - 10)^2 =>

2 * 2^2 + 3 * 0^2 + (-1)^2 + (-3)^2 =>

2 * 4 + 3 * 0 + 1 + 9 =>

8 + 0 + 1 + 9 =>

18

Divide that by the number of values in the set

18/7

That's the variance. The standard deviation is the square root of that

sqrt(18/7) =>

sqrt(18 * 7 / 49) =>

sqrt(9/49) * sqrt(2 * 7) =>

3 * sqrt(14) / 7