# How to find the standard error of mean in R?

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The standard error of mean is the standard deviation divided by the square root of the sample size. The easiest way to find the standard error of mean is using the formula to find its value.

## Example

> set.seed(1)

We will find the standard errors for a normal random variable, sequence of numbers from one to hundred, a random sample, a binomial random variable, and uniform random variable using the same formula. And at the end, I will confirm whether we used the correct method or not for all types of variables we have considered here.

> x<-rnorm(10)
> x
[1] -0.6264538 0.1836433 -0.8356286  1.5952808 0.3295078 -0.8204684
[7]  0.4874291 0.7383247  0.5757814 -0.3053884
> SE_x<-sd(x)/sqrt(10)
> SE_x
[1] 0.246843
> y<-1:100
> y
[1]   1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18
[19] 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
[37] 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54
[55] 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72
[73] 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90
[91] 91 92 93 94 95 96 97 98 99 100
> SE_y<-sd(y)/sqrt(100)
> SE_y
[1] 2.901149
> z<-sample(1:100,20,replace=TRUE)
> z
[1] 73 79 85 37 89 37 34 89 44 79 33 84 35 70 74 42 38 20 28 20
> SE_z<-sd(z)/sqrt(20)
> SE_z
[1] 5.582161
> a<-rbinom(20,100,0.6)
> a
[1] 63 66 59 58 48 66 59 65 60 56 55 55 56 57 56 66 53 62 61 51
> SE_a<-sd(a)/sqrt(20)
> SE_a
[1] 1.141098
> b<-runif(30,2,5)
> b
[1]  4.928512 4.195378 3.070181 3.294421 2.444635 2.039233 4.146698 2.309553
[9]  3.338853 3.920303 4.975516 3.486781 3.453049 2.520327 4.264463 3.361686
[17] 3.533509 2.622635 2.685974 3.787136 3.724617 2.231193 2.106622 3.928386
[25] 4.785846 3.794277 3.682702 3.578083 4.955286 3.522925
> SE_b<-sd(b)/sqrt(30)
> SE_b
[1] 0.1552736
> c<-sample(20)
> c
[1] 19 4 2 16 1 12 7 9 15 10 11 18 13 3 17 8 14 20 6 5
> SE_c<-sd(c)/sqrt(20)
> SE_c
[1] 1.322876

If we don’t know the sample size then we can use length function as follows −

> SE_c<-sd(c)/sqrt(length(c))
> SE_c
[1] 1.322876

Here, the standard error for uniform random variable and binomial random variable are not correct because their standard deviations are not calculated by sd function.

Updated on 10-Aug-2020 14:03:41