Population Variance, Standard deviation and coefficient of variation for grouped data calculator

Solution

Problem: Population Variance {{10-20,15},{20-30,25},{30-40,20},{40-50,12},{50-60,8}} [ Calculator, Method and examples ]

Solution:
Your problem `->` Population Variance {{10-20,15},{20-30,25},{30-40,20},{40-50,12},{50-60,8}}

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)`	`f*d^2` `(6)=(5)xx(4)`
10 - 20	15	15	-2	-30	60
20 - 30	25	25	-1	-25	25
30 - 40	20	35=A	0	0	0
40 - 50	12	45	1	12	12
50 - 60	8	55	2	16	32
---	---	---	---	---	---
	`n = 80`	-----	-----	*`sum fd=-27`**	*`sum fd^2=129`**

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

`=35 + (-27)/80 * 10`

`=35 + (-0.3375) * 10`

`=35 -3.375`

`=31.625`

Population Variance `sigma^2 = ((sum f*d^2 - (sum f*d)^2/n)/n) * h^2`

`=((129 - (-27)^2/80)/80) * 10^2`

`=((129 - 9.1125)/80) * 100`

`=119.8875/80 * 100`

`=1.4986 * 100`

`=149.8594`

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