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6-8 Measures of Central Tendency and Variation
Objective
• Find measures of central tendency and measures of variation for statistical data.
• Examine the effects of outliers on statistical data.
The symbol commonly used to represent the mean is x, or “x bar.”
The symbol for standard deviation is the lowercase Greek letter sigma, σ.
Reading Math
Small standard deviations indicate data clustered near the meanLarge standard deviations indicate data is spread out
Step 1: Find the mean xStep 2: Find the difference between mean
and each data value Step 3: Square each of the values from step 2
Step 4: Add all of the values from step 3 and
divide by the # of data -1 (n - 1). This
is variance
Step 5: Take the square root of the variance
to find the standard deviation
Finding Standard Deviation
Example 1: Finding the Mean and Standard Deviation
Find the mean and standard deviation for the data set of the number of people getting on and off a bus for several stops.
{6, 8, 7, 5, 9}
Step 1 Find the mean.
6 8 7 5 9x
____
Step 2 Find the difference between the mean and each data value, and square it.
Data value (x) 6 8 7 5 9
x x 2x x
Example 1: Finding the Mean and Standard Deviation
Find the mean and standard deviation for the data set of the number of people getting on and off a bus for several stops.
{6, 8, 7, 5, 9}
Step 1 Find the mean.
6 8 7 5 9
5x
7
Step 2 Find the difference between the mean and each data value, and square it.
Data value (x) 6 8 7 5 9
x x 2x x
0-101
1 1
-2 4
24
Example 1 Continued
Step 3 Find the variance.Find the average of the last row of the table
Step 4 Find the standard deviation.
The standard deviation is the square root of the variance
The mean is 7 peoplethe standard deviation
Data value (x) 6 8 7 5 9
x x 2x x
0-101
1 1
-2 4
24
variance
standarddeviation
Example 1 Continued
Step 3 Find the variance.Find the average of the last row of the table
Step 4 Find the standard deviation.
The standard deviation is the square root of the variance
The mean is 7 peoplethe standard deviation
Data value (x) 6 8 7 5 9
x x 2x x
0-101
1 1
-2 4
24
1 1 0 4 4variance
5 1
2.5
standard deviation 2.5
Example 2
Find the mean and standard deviation for the data set of the number of elevator stops for several rides.
{0, 4, 2, 1, 6, 5}
Step 1 Find the mean.
0 4 2 1 6 5x
______
Step 2 Find the difference between the mean and each data value, and square it.
Data value (x) 0 4 2 1 6 5
x x 2x x
Example 2
Find the mean and standard deviation for the data set of the number of elevator stops for several rides.
{0, 4, 2, 1, 6, 5}
Step 1 Find the mean.
0 4 2 1 6 5x
______
Step 2 Find the difference between the mean and each data value, and square it.
Data value (x) 0 4 2 1 6 5
x x 2x x
-1-311
1 9
-2 4
24
39
Example 2 Continued
Find the average of the last row of the table
Step 4 Find the standard deviation.
The standard deviation is the square root of the variance
The mean is __, and the standard deviation is
9 1 1 4 9 4variance
_____
standarddeviation
Data value (x) 0 4 2 1 6 5
x x 2x x
-1-311
1 9
-2 4
24
39
Step 3 Find the variance.
Example 2 Continued
Find the average of the last row of the table
Step 4 Find the standard deviation.
The standard deviation is the square root of the variance
The mean is 3, and the standard deviation is
9 1 1 4 9 4variance
6 1
5.6
standard deviation 5.6
Data value (x) 0 4 2 1 6 5
x x 2x x
-1-311
1 9
-2 4
24
39
Step 3 Find the variance.
Classwork/Homework
6-8 Worksheet
