Find missing frequency for grouped data Find 1 Missing frequency when Mean is given example

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Home > Statistical Methods calculators > Find missing frequency for grouped data example

Find missing frequency for grouped data ( Enter your problem )

( Enter your problem )

Find 1 Missing frequency when Mean is given example
Find 1 Missing frequency when Median is given example
Find 2 Missing frequencies when Mean is given example
Find 2 Missing frequencies when Median is given example
Find 2 Missing frequencies when Mode is given example
Find 2 Missing frequencies when Quartile is given example
Find 3 Missing frequencies when Mean or Median or mode are given example

2. Find 1 Missing frequency when Median is given example
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1. Find 1 Missing frequency when Mean is given example

1. Find missing frequency from the following data
Class Frequency
5 - 10 11
10 - 15 20
15 - 20 35
20 - 25 20
25 - 30 a
30 - 35 6
mean = 18.1

Solution:

Class `(1)`	Frequency `(f)` `(2)`	Mid value `(x)` `(3)`	`d=(x-A)/h=(x-27.5)/5` `A=27.5,h=5` `(4)`	`f*d` `(5)=(2)xx(4)`
5 - 10	11	7.5 `7.5=(5+10)/2`	-4 `d=(7.5-27.5)/5=(-20)/5=-4` `d=(x-27.5)/5`	`-44` `-44=11xx-4` `(5)=(2)xx(4)`
10 - 15	20	12.5 `12.5=(10+15)/2`	-3 `d=(12.5-27.5)/5=(-15)/5=-3` `d=(x-27.5)/5`	`-60` `-60=20xx-3` `(5)=(2)xx(4)`
15 - 20	35	17.5 `17.5=(15+20)/2`	-2 `d=(17.5-27.5)/5=(-10)/5=-2` `d=(x-27.5)/5`	`-70` `-70=35xx-2` `(5)=(2)xx(4)`
20 - 25	20	22.5 `22.5=(20+25)/2`	-1 `d=(22.5-27.5)/5=(-5)/5=-1` `d=(x-27.5)/5`	`-20` `-20=20xx-1` `(5)=(2)xx(4)`
25 - 30	a	27.5 `27.5=(25+30)/2`	0 `d=(27.5-27.5)/5=(0)/5=0` `d=(x-27.5)/5`	`0` `0=axx0` `(5)=(2)xx(4)`
30 - 35	6	32.5 `32.5=(30+35)/2`	1 `d=(32.5-27.5)/5=(5)/5=1` `d=(x-27.5)/5`	`6` `6=6xx1` `(5)=(2)xx(4)`
---	---	---	---	---
	`n=92+a`	-----	-----	`sum f*d=-188`

Mean `bar x = A + (sum fd)/n * h`

`18.1 = 27.5 + (-188)/(92+a) * 5`

`-9.4 = (-188)/(92+a) * 5`

`92+a = (-188)/(-9.4) * 5`

`92+a = 100`

`a = 100 - 92`

`a = 8`

Thus, the missing frequency is `8`.

2. Find missing frequency from the following data
Class Frequency
100 - 110 100
110 - 120 130
120 - 130 71
130 - 140 20
140 - 150 ?
150 - 160 50
mean = 123

Solution:

Class `(1)`	Frequency `(f)` `(2)`	Mid value `(x)` `(3)`	`d=(x-A)/h=(x-145)/10` `A=145,h=10` `(4)`	`f*d` `(5)=(2)xx(4)`
100 - 110	100	105	-4	`-400`
110 - 120	130	115	-3	`-390`
120 - 130	71	125	-2	`-142`
130 - 140	20	135	-1	`-20`
140 - 150	a	145	0	`0`
150 - 160	50	155	1	`50`
---	---	---	---	---
	`n=371+a`	-----	-----	`sum f*d=-902`

Mean `bar x = A + (sum fd)/n * h`

`123=145 + (-902)/(371+a) * 10`

`-22 = (-902)/(371+a) * 10`

`371+a = (-902)/(-22) * 10`

`371+a=410`

`a=410 - 371`

`a=39`

Thus, the missing frequency is `39`.

3. Find missing frequency from the following data
Class Frequency
0 - 10 4
10 - 20 4
20 - 30 9
30 - 40 ?
40 - 50 12
50 - 60 6
60 - 70 3
70 - 80 2
mean = 37

Solution:

Class `(1)`	Frequency `(f)` `(2)`	Mid value `(x)` `(3)`	`d=(x-A)/h=(x-35)/10` `A=35,h=10` `(4)`	`f*d` `(5)=(2)xx(4)`
0 - 10	4	5	-3	`-12`
10 - 20	4	15	-2	`-8`
20 - 30	9	25	-1	`-9`
30 - 40	a	35	0	`0`
40 - 50	12	45	1	`12`
50 - 60	6	55	2	`12`
60 - 70	3	65	3	`9`
70 - 80	2	75	4	`8`
---	---	---	---	---
	`n=40+a`	-----	-----	`sum f*d=12`

Mean `bar x = A + (sum fd)/n * h`

`37=35 + (12)/(40+a) * 10`

`2 = (12)/(40+a) * 10`

`40+a = (12)/(2) * 10`

`40+a=60`

`a=60 - 40`

`a=20`

Thus, the missing frequency is `20`.

This material is intended as a summary. Use your textbook for detail explanation.
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