Sample Variance, Standard deviation and coefficient of variation for mixed data calculator

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Home > Statistical Methods calculators > Sample Variance, Standard deviation and coefficient of variation for mixed data calculator

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Find Sample Variance, Standard deviation and coefficient of variation for mixed data

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Mean	Quartile
Median	Deciles
Mode	Percentiles

Population Variance `(sigma^2)`	Sample Variance `(S^2)`
Population Standard deviation `(sigma)`	Sample Standard deviation `(S)`
Population Coefficient of Variation	Sample Coefficient of Variation

Class 1 2 5 6 - 10 10 - 20 20 - 30 30 - 50 50 - 70 70 - 100
Frequency 3 4 10 23 20 20 15 3 2
Class 2 3 4 5 - 9 10 - 14 15 - 19 20 - 29
Frequency 1 2 2 8 15 8 4

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Solution

Solution provided by AtoZmath.com

Sample Variance, Standard deviation and coefficient of variation for mixed data calculator

1. Calculate the mean and standard deviation for the following distribution

Class	1	2	5	6-10	10-20	20-30	30-50	50-70	70-100
f	3	4	10	23	20	20	15	3	2

Example

1. Calculate Sample Variance `(S^2)` from the following mixed data
Class Frequency
1 3
2 4
5 10
6 - 10 23
10 - 20 20
20 - 30 20
30 - 50 15
50 - 70 3
70 - 100 2

Solution:

Class `(1)`	Frequency `(f)` `(2)`	Mid value `(x)` `(3)`	`f*x` `(4)=(2)xx(3)`	`fx^2=(fx)xx(x)` `(5)=(4)xx(3)`
1	3	1	3	3
2	4	2	8	16
5	10	5	50	250
6 - 10	23	8	184	1472
10 - 20	20	15	300	4500
20 - 30	20	25	500	12500
30 - 50	15	40	600	24000
50 - 70	3	60	180	10800
70 - 100	2	85	170	14450
---	---	---	---	---
	`n = 100`	-----	`sum f*x=1995`	`sum f*x^2=67991`

Mean `bar x = (sum fx)/n`

`=1995/100`

`=19.95`

Sample Variance `S^2 = (sum f*x^2 - (sum f*x)^2/n)/(n-1)`

`=(67991 - (1995)^2/100)/99`

`=(67991 - 39800.25)/99`

`=28190.75/99`

`=284.7551`

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