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8/2/2019 3.3 Mean and Standard Deviation of Grouped Data
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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.
8/2/2019 3.3 Mean and Standard Deviation of Grouped Data
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Sample Mean for a Frequency
Distribution
x = class midpoint
n
xfx
8/2/2019 3.3 Mean and Standard Deviation of Grouped Data
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Sample Standard Deviation for
a Frequency Distribution
1
)( 2
n
fxxs
8/2/2019 3.3 Mean and Standard Deviation of Grouped Data
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Computation Formula for
Standard Deviation for aFrequency Distribution
n
xf
fx
n
SS
sx
2
2
xSSwhere
1
8/2/2019 3.3 Mean and Standard Deviation of Grouped Data
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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