Standard deviation

From Wikipedia, the free encyclopedia

Standard deviation is a concept in statistics that tells you how spread out a set of values is. It can be calculated by considering how far away each value is from the average of all the values.

Standard deviation can be used to measure how consistent or how precise a set of data is.

[change] Method

In a set of values, you find the standard deviation by following these steps:

1. Find the average of all the values.
2. Subtract the average from each value, giving you their deviations.
3. Square the deviation for each value.
4. Find the average of all these squared deviations.
5. Find the square root of that average.

[change] Example

We can find the standard deviation of the numbers 3, 7, 7 and 19 as follows.

Step 1: find the average of 3, 7, 7, and 19:

(3 + 7 + 7 + 19) / 4 = 9.

Step 2: find the deviation of each number from the average:

3 − 9 = − 6

7 − 9 = − 2

7 − 9 = − 2

19 − 9 = 10.

Step 3: square each of the deviations:

( − 6)² = 36

( − 2)² = 4

( − 2)² = 4

10² = 100.

Step 4: find the mean of those squared deviations:

(36 + 4 + 4 + 100) / 4 = 36.

Step 5: find the square root:

So, the standard deviation is 6.

[change] Other websites

• "Standard Deviation and Variance," Maths Is Fun