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September 8, 2010

Statistics Notes — Variance and Standard Deviation for Grouped Data

Filed under: Statistics, Statistics Notes — Tags: — bowman @ 9:58 am

Variance and Standard Deviation for Grouped Data

You may be faced with finding the variance and standard deviation of data that has been collected and organized into a frequency distribution table and may not have access to the original data.

Here’s how we work with the data in the distribution table.

Here’s an example of organized data.

The amount of caffeine in a sample of 5-ounce servings of brewed coffee is given in the distribution table. Use this data to estimate the samples mean, variance, and standard deviation.

Classes

Frequency

60 – 81

1

82 – 103

12

104 – 125

25

126 – 147

10

148 – 169

2

Use the midpoint of each class to represent the entire class. Assign weight.

Classes

Frequency

Midpoint, x

f . x

60 – 81

1

70.5

70.5

82 – 103

12

92.5

1110

104 – 125

25

114.5

2862.5

126 – 147

10

136.5

1365

148 – 169

2

158.5

317

Classes

Frequency

Midpoint, x

60 – 81

1

70.5

-44

82 – 103

12

92.5

-22

104 – 125

25

114.5

0

126 – 147

10

136.5

22

148 – 169

2

158.5

44

.
Next, find the square of the deviations and assign weight.

Classes

Frequency

Midpoint, x

60 – 81

1

70.5

-44

1936

1936

82 – 103

12

92.5

-22

484

5808

104 – 125

25

114.5

0

0

0

126 – 147

10

136.5

22

484

4840

148 – 169

2

158.5

44

1936

3872

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