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Population Variance, Standard deviation and coefficient of variation for mixed data Formula & Example ( Enter your problem )
  1. Formula & Example
  2. Population Variance Example
  3. Population Standard deviation Example
  4. Population coefficient of variation Example
Other related methods
  1. Mean, Median and Mode
  2. Population Variance, Standard deviation and coefficient of variation
  3. Sample Variance, Standard deviation and coefficient of variation

1. Mean, Median and Mode
(Previous method)
2. Population Variance Example
(Next example)

1. Formula & Example





Formula
1. Mean ˉx=fxn
2. Population Variance σ2=fx2-(fx)2nn
3. Population Standard deviation σ=fx2-(fx)2nn
4. Coefficient of Variation (Population) =σˉx100%

Examples
1. Calculate Population Variance (σ2), Population Standard deviation (σ), Population Coefficient of Variation from the following mixed data
ClassFrequency
13
24
510
6 - 1023
10 - 2020
20 - 3020
30 - 5015
50 - 703
70 - 1002


Solution:
Class
(1)
Frequency (f)
(2)
Mid value (x)
(3)
fx
(4)=(2)×(3)
fx2=(fx)×(x)
(5)=(4)×(3)
13 1 1=1 3 3=3×1
(4)=(2)×(3)
 3 3=3×1
(5)=(4)×(3)
24 2 2=2 8 8=4×2
(4)=(2)×(3)
 16 16=8×2
(5)=(4)×(3)
510 5 5=5 50 50=10×5
(4)=(2)×(3)
 250 250=50×5
(5)=(4)×(3)
6 - 1023 8 8=6+102 184 184=23×8
(4)=(2)×(3)
 1472 1472=184×8
(5)=(4)×(3)
10 - 2020 15 15=10+202 300 300=20×15
(4)=(2)×(3)
 4500 4500=300×15
(5)=(4)×(3)
20 - 3020 25 25=20+302 500 500=20×25
(4)=(2)×(3)
 12500 12500=500×25
(5)=(4)×(3)
30 - 5015 40 40=30+502 600 600=15×40
(4)=(2)×(3)
 24000 24000=600×40
(5)=(4)×(3)
50 - 703 60 60=50+702 180 180=3×60
(4)=(2)×(3)
 10800 10800=180×60
(5)=(4)×(3)
70 - 1002 85 85=70+1002 170 170=2×85
(4)=(2)×(3)
 14450 14450=170×85
(5)=(4)×(3)
---------------
n=100-----fx=1995fx2=67991


Mean ˉx=fxn

=1995100

=19.95



Population Variance σ2=fx2-(fx)2nn

=67991-(1995)2100100

=67991-39800.25100

=28190.75100

=281.9075



Population Standard deviation σ=fx2-(fx)2nn

=67991-(1995)2100100

=67991-39800.25100

=28190.75100

=281.9075

=16.7901



Coefficient of Variation (Population) =σˉx100%

=16.790119.95100%

=84.16%
2. Calculate Population Variance (σ2), Population Standard deviation (σ), Population Coefficient of Variation from the following mixed data
ClassFrequency
21
32
42
5 - 98
10 - 1415
15 - 198
20 - 294


Solution:
Class
(1)
Frequency (f)
(2)
Mid value (x)
(3)
fx
(4)=(2)×(3)
fx2=(fx)×(x)
(5)=(4)×(3)
21224
323618
424832
5 - 98756392
10 - 1415121802160
15 - 198171362312
20 - 29424.5982401
---------------
n=40-----fx=486fx2=7319


Mean ˉx=fxn

=48640

=12.15



Population Variance σ2=fx2-(fx)2nn

=7319-(486)24040

=7319-5904.940

=1414.140

=35.3525



Population Standard deviation σ=fx2-(fx)2nn

=7319-(486)24040

=7319-5904.940

=1414.140

=35.3525

=5.9458



Coefficient of Variation (Population) =σˉx100%

=5.945812.15100%

=48.94%


This material is intended as a summary. Use your textbook for detail explanation.
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1. Mean, Median and Mode
(Previous method)
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