Download CALCULATING STANDARD DEVIATION WORKSHEET

CALCULATING STANDARD DEVIATION WORKSHEET
The standard deviation is used to tell how scores scatter around the mean. The smaller the
standard deviation, the more closely the scores cluster around the mean. When the standard
deviation is large, the scores are more widely scattered.
The standard deviation is calculated as the average distance from the mean.
Example Problem:
The junior high baseball team played ten baseball games. Find the standard deviation for the
runs scored by the team for the ten games, 5 , 1 , 5 , 6 , 7 , 7 , 2 , 4 , 8 , 5
Follow the steps below to calculate the standard deviation
Step 1: Arrange the scores in the Score column of the table below in order from the smallest to the largest.
Step 2: Find the mean of the data set and place your answer below on Line A.
Step 3:Subtract the mean from each of the scores. Record the differences in the Difference From Mean column in
the table below. Be sure to record whether the answer is positive or negative. (i.e.: 4  5  1,7  5  2 )
Step 4: Find the square of each number in the Difference From Mean column and record the result in the Square of
Difference column (i.e.: (1)  1 )
Step 5: The number of items in the data set is labeled n. Record the number of items minus 1 in this data set on Line
B below. n-1 is called the Degree of Freedom.
Step 6: Find the sum of the numbers in the Square of Difference and record your answer in the table .
Step 7: Take the Sum of the (Difference from the Mean)2 and divide it by n-1. Record your answer on Line C
below.
Step 8: The square root of Line C is the standard deviation. Record your answer on Line D below
2
Difference from the
Mean
Score
(Difference from the
Mean)2
Sum of (Difference
from the Mean)2
A. Mean: _________
B. n-1: ___________
C. Sum of (Difference from the Mean)2 divided by (n-1):_________________
 (diff .fromMean) 2 
 is ________________
D. Standard deviation 


n 1


Practice Problems
1. Find the standard deviation for the following data. Use the chart below to record the steps.
80, 100, 92, 90, 96, 94
Difference from the
Mean
Score
(Difference from the
Mean)2
Sum of (Difference
from the Mean)2
A. Mean: _________
B. n-1: ___________
C. Sum of (Difference from the Mean)2 divided by (n-1):_________________
 (diff .fromMean) 2 
 is ________________
D. Standard deviation 


n 1


2. The standard deviation is a measure of ___________________.
3. The standard deviation is used to find the variability or how the numbers in a group
______________ around the ______________.
The term +1 standard deviation is read "one standard deviation above the mean." To find
the score that is +1 standard deviation above the mean, add the standard deviation to the
mean of the data set. The same applies to -1 standard deviation (one standard deviation
below the mean) except you subtract the standard deviation from the mean. For questions
4-6, refer to the scores in the baseball example on the front of this page.
4. List the three scores that are within +1 standard deviation of the mean. ________________.
5. List the one score that is within -1 standard deviation of the mean. _________________.
6. The scores that are between -2 and +2 standard deviations of the mean are:
________________________________________