Standard deviation

From Wikipedia, the free encyclopedia

Standard deviation is a concept from statistics. It tells how the values are grouped around the mean. It is the average of a set of numbers' difference from the mean.

[change] Method

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

1. Find the mean of all the data points.
2. Subtract the mean from each data point.
3. Square the deviation for each data point.
4. Average all these squared deviations.
5. Find the square root.

Standard deviation can be used to evaluate the precision or consistency of a set of data. Standard deviation can also produce standard error, which is useful in statistical inference.

[change] Example

To find the standard deviation of the numbers 3, 7, 7, and 19.

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

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

Step 2: find the deviation of each number from the mean,

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