6.3. Standard Deviation of a Data Set http://www.ck12.org
Guided Practice
Calculate the standard deviation of the following numbers, which represent a small population:
2 , 7 , 5 , 6 , 4 , 2 , 6 , 3 , 6 , 9
Answer:
Step 1:It is not necessary to organize the data. Create a table and label each of the columns appropriately. Write
the data values in columnx.
Step 2:Calculate the mean of the data values.
μ=2 + 7 + 5 + 6 + 4 + 2 + 6 + 3 + 6 + 9
10
=
50
10
= 5. 0
Step 3:Calculate the differences between the data values and the mean. Enter the results in the second column.
TABLE6.17:
x (x−μ)
2 − 3
7 2
5 0
6 1
4 − 1
2 − 3
6 1
3 − 2
6 1
9 4Step 4:Calculate the values for column 3 by squaring each result in the second column.
TABLE6.18:
(x−μ)^2
9 4 0 1 1 9 1 4 116
Step 5:Calculate the mean of the third column and then take the square root of the answer. This value is the standard
deviation(σ)of the data set.