CK-12 Basic Probability and Statistics - A Short Course

http://www.ck12.org Chapter 5. The Shape, Center and Spread of a Normal Distribution - Basic

HINT: If you are wondering if your calculations are correct, a quick way to check is to add the values in the(x−x ̄)
column. The total is always zero.

Example 3:

Calculate the standard deviation of the following numbers:

1 , 5 , 3 , 5 , 4 , 2 , 1 , 1 , 6 , 2

Solution:

TABLE5.3:

x (x−x ̄) (x−x ̄)^2

1 -2 4

5 2 4

3 0 0

5 2 4

4 1 1

2 -1 1

1 -2 4

1 -2 4

6 3 9

2 -1 1

∑x=^30 σ=

√

∑(x−x ̄)^2

n

x ̄=

30

10

σ=

√

32

10

x ̄= 3 σ=

√

3. 2

σ= 1. 8

Now that you know how to calculate the variance and the standard deviation of a set of data, let’s apply this to normal
distribution, by determining how your Math mark compared to the marks achieved by your classmates. This time
technology will be used to determine both the variance and the standard deviation of the data.

Solution: