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Mean and Standard Deviation of

Grouped Data Make a frequency table

Compute the midpoint (x) for each class.

Count the number of entries in each class

(f).

Sum the f values to find n, the total number

of entries in the distribution.

Treat each entry of a class as if it falls at the

class midpoint.

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Sample Mean for a Frequency

Distribution

x = class midpoint

n

xfx

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Sample Standard Deviation for

a Frequency Distribution

1

)( 2

n

fxxs

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Computation Formula for

Standard Deviation for aFrequency Distribution

n

xf

fx

n

SS

sx

2

2

xSSwhere

1

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Calculation of the mean of

grouped data

Ages: f

30 - 34 4

35 - 39 5

40 - 44 2

45 - 49 9

x

32

37

42

xf

128

185

84

xf = 820f = 20

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Mean of Grouped Data

f

xf

n

xfx

0.4120

820

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Calculation of the standard

deviation of grouped data

Ages: f

30 - 34 4

35 - 39 5

40 - 44 2

45 - 49 9

x

32

37

42

47

xmean

9

4

1

6

Mean

(xmean)2

81

16

1

36

(xmean)2 f

324

80

2

324

f = 20(xmean)2 f =

730

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Calculation of the standard

deviation of grouped data

f = n = 20

20.642.38120

730

1

)(2

n

fxxs

7302 xx

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Computation Formula for

Standard Deviation for aFrequency Distribution

n

xf

fx

n

SS

sx

2

2

xSSwhere

1

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Computation Formula for

Standard Deviation

f

4

5

2

9

x

32

37

42

xf

128

185

84

xf = 820f = 20

x2f

4096

6845

3528

19881

x2f =34350

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Computation Formula for

Standard Deviation for aFrequency Distribution

20.6120

730

1

730

20

82034350

SSwhere

2

2

2x

n

SSs

nxffx

x

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Weighted Average

Average calculated where some of

the numbers are assigned moreimportance or weight

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Weighted Average

x.valuedatatheofweightthew

AverageWeighted

where

w

xw

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Compute the Weighted Average:

Midterm grade = 92

Term Paper grade = 80

Final exam grade = 88

Midterm weight = 25%

Term paper weight = 25% Final exam weight = 50%

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Compute the Weighted Average:

x w xw

Midterm 92 .25 23

Term Paper 80 .25 20

Final exam 88 .50 44

1.00 87

AverageWeighted8700.1

87

w

xw