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