Mean: 10 Variance: 19.8 Standard Deviation: Approximately 4.45
Practice makes perfect
We want to find the mean, variance, and standard deviation of the given data set.
5, 15, 9, 3, 12, 8, 13, 6, 18, 11
Let's find each statistic one at a time.
Mean
The mean of a data set x is calculated by finding the sum of all of the values in the set and then dividing by the number of values in the set. In this case, there are 10 values.
Now we will find the standard deviation. The standard deviation is a measure of variation which shows how much data values deviate from the mean. Since we already know the mean, we will follow four steps in finding the standard deviation.
Note that we subtract the mean from each data value in Step 1 of finding the standard deviation. To calculate the squared differences between the mean and the data values, we will use a table.
x
x
x-x
(x-x)^2
5
10
- 5
25
15
10
5
25
9
10
- 1
1
3
10
- 7
49
12
10
2
4
8
10
- 2
4
13
10
3
9
6
10
- 4
16
18
10
8
64
11
10
1
1
Sum of Values
198
Next we need to find the variance σ^2, which is the mean of the squared differences. To calculate it we will use the sum obtained in the table.
