# How to calculate population variance in R?

There is no function in R to calculate the population variance but we can use the population size and sample variance to find it. We know that the divisor in population variance is the population size and if we multiply the output of var(it calculates sample variance) function with (population size – 1)/population size then the output will be population variance.

## Example

Live Demo

set.seed(141)
x1<-1:100
Sample_Variance<-var(x1)
Sample_Variance

## Output

[1] 841.6667

## Example

Population_Variance<-var(x1)*(99/100)
Population_Variance

## Output

[1] 833.25

## Example

Live Demo

x2<-rnorm(500)
Sample_Variance<-var(x2)
Sample_Variance

## Output

[1] 1.013514

## Example

Population_Variance<-var(x2)*(499/500)
Population_Variance

## Output

[1] 1.011487

## Example

Live Demo

x3<-round(rnorm(500),0) Sample_Variance<-var(x3)
Sample_Variance

## Output

[1] 1.088401

## Example

Population_Variance<-var(x3)*(499/500)
Population_Variance

## Output

[1] 1.086224

## Example

Live Demo

x4<-rpois(150,10)
x4

## Output

[1] 15 13 11 4 10 9 13 12 8 12 7 13 10 18 8 11 15 8 9 14 7 14 8 11 7
[26] 6 10 12 7 15 13 12 13 11 9 7 15 11 17 10 17 11 9 10 17 11 4 11 11 9
[51] 11 10 11 10 16 11 6 4 9 5 5 6 6 6 10 10 10 13 10 6 10 9 7 11 13
[76] 12 7 5 10 7 7 10 7 10 10 14 11 11 9 6 13 9 5 11 13 11 10 10 6 15
[101] 7 12 7 9 13 6 9 13 13 11 11 16 5 12 14 10 10 10 13 7 4 16 6 13 6
[126] 4 9 7 9 7 8 12 12 10 10 9 8 4 10 8 9 7 13 7 11 9 8 8 10 12

## Example

Sample_Variance<-var(x4)
Sample_Variance

## Output

[1] 10.86694

## Example

Population_Variance<-var(x4)*(149/150)
Population_Variance

## Output

[1] 10.79449

## Example

Live Demo

x5<-sample(1:100,120,replace=TRUE)
x5

## Output

[1] 62 59 25 15 16 17 69 22 81 90 91 68 61 40 61 48 33 71 60 11 1 15 95 17 81
[26] 29 16 44 47 26 20 56 97 74 3 5 44 77 50 44 83 54 37 54 73 46 99 19 85 28
[51] 8 49 15 80 65 50 85 7 91 76 83 93 54 95 52 8 20 18 70 12 66 36 2 99 81
[76] 13 91 11 73 19 2 73 20 12 80 41 38 20 61 64 39 30 65 28 25 38 56 61 44 32
[101] 66 76 2 72 36 78 48 41 52 17 31 69 33 74 39 60 29 59 72 11

## Example

Sample_Variance<-var(x5)
Sample_Variance

## Output

[1] 892.7361

## Example

Population_Variance<-var(x5)*(119/120)
Population_Variance

## Output

[1] 885.2966

## Example

Live Demo

x6<--sample(101:999,120)
x6

## Output

[1] -919 -502 -343 -523 -867 -405 -368 -447 -286 -578 -147 -665 -823 -598 -260
[16] -740 -569 -661 -386 -267 -185 -114 -608 -711 -638 -992 -552 -795 -291 -152
[31] -154 -211 -721 -388 -283 -234 -525 -942 -599 -176 -239 -788 -579 -875 -883
[46] -856 -143 -304 -407 -448 -717 -524 -273 -235 -167 -158 -659 -432 -803 -624
[61] -187 -312 -225 -802 -439 -453 -637 -571 -768 -664 -473 -331 -806 -265 -173
[76] -748 -623 -671 -989 -888 -950 -589 -487 -526 -668 -760 -414 -622 -248 -276
[91] -139 -951 -630 -885 -440 -191 -491 -685 -653 -132 -742 -477 -181 -505 -759
[106] -974 -741 -548 -593 -240 -527 -914 -402 -127 -860 -336 -333 -794 -891 -311

## Example

Sample_Variance<-var(x6)
Sample_Variance

## Output

[1] 62657.78

## Example

Population_Variance<-var(x6)*(119/120)
Population_Variance

## Output

[1] 62135.63

## Example

Live Demo

x7<-rexp(50,3.5)
x7

## Output

[1] 0.205216964 0.133222130 0.488146733 0.244428905 0.833206350 0.069545948
[7] 0.195504191 0.539364253 1.099099582 1.835459402 0.170821138 0.342813864
[13] 0.108211014 0.392889843 0.069053900 0.083381383 0.282172880 1.299693448
[19] 0.033847926 0.248126373 0.537849065 0.508127648 0.148564885 0.047607303
[25] 0.247224701 0.171349073 0.089745700 0.157843010 0.870047906 0.790377494
[31] 0.285218089 0.107768506 0.806453962 0.565196530 0.283891426 0.129423319
[37] 0.116770751 0.238833628 0.379741206 0.009492331 0.343673059 0.072587659
[43] 0.076498866 0.504828741 0.313257385 0.427818704 0.372741859 0.210799536
[49] 0.155322546 0.504289020

## Example

Sample_Variance<-var(x7)
Sample_Variance

## Output

[1] 0.03401862

## Example

Population_Variance<-var(x7)*(49/50)
Population_Variance

## Output

[1] 0.03333825

Updated on: 10-Oct-2020

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