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

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

10​, 9​, 7​, 12​, 22

The range is____

The standard deviation is_____

Relevance
• The range you should be able to do just by inspection. The range is the difference between the largest and smallest value.

largest = 22

smallest = 7

22 - 7 = 15

The range is 15.

To find the standard deviation, first you need to find the mean (the average) of the 5 numbers.

(10 + 9 + 7 + 12 + 22) / 5

= 12

Now take the difference between each number and the mean and square it.

10 - 12 = -2 --> (-2)² = 4

9 - 12 = -3 --> (-3)² = 9

7 - 12 = -5 --> (-5)² = 25

12 - 12 = 0 --> 0² = 0

22 - 12 = 10 --> 10² = 100

Add up all those results and divide by how many numbers you have (5):

(4 + 9 + 25 + 0 + 100) / 5

= 138 / 5

= 27.6

That's what is known as the *variance*.

var = 27.6

To find the standard deviation, you take the square root of the variance.

σ = √27.6

σ ≈ 5.25357

P.S. I'm assuming this is the complete data set and so you want the standard deviation for the *population*.

There is a slightly different formula if this is the standard deviation of a *sample*. In that case after adding up the squares, you divide by *one less than* how many numbers you have:

sample variance = 138 / 4 = 34.5

Then take the square root of that:

sample s.d. = √34.5 ≈ 5.87367

But given that this is said to be "the set of data" I'm assuming it is the complete population and the first value (5.25357) is correct.

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

10​, 9​, 7​, 12​, 22

The range is 15

The standard deviation is 5.8737

• The range is from 7 to 22

The standard deviation is 5.87367

You're supposed to use the formula to solve for Standard Deviation, but I used an online calculator