# 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

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• 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.

• 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