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 DeviationFind 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 DeviationFind 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 95

x 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 9x 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 9x x 2x x

0-101

1 1

-2 4

24

1 1 0 4 4variance5 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 5x 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 4variance6 1

5.6

standard deviation 5.6

Data value (x) 0 4 2 1 6 5x x 2x x

-1-311

1 9

-2 4

24

39

Step 3 Find the variance.

Classwork/Homework

6-8 Worksheet