See code and explanation below.
Step-by-step explanation:
For this case we can use the following R code to create a vector of 100 elements from a normal distribution given by:
The function rnorm creates a sample data from the normla distribution with the mean and deviation provided
> normal<-rnorm(100,mean = 100,sd=20)
We can visualize the data like this
> normal
[1] 87.47092 103.67287 83.28743 131.90562 106.59016 83.59063 109.74858 114.76649 111.51563
[10] 93.89223 130.23562 107.79686 87.57519 55.70600 122.49862 99.10133 99.67619 118.87672
[19] 116.42442 111.87803 118.37955 115.64273 101.49130 60.21297 112.39651 98.87743 96.88409
[28] 70.58495 90.43700 108.35883 127.17359 97.94425 107.75343 98.92390 72.45881 91.70011
[37] 92.11420 98.81373 122.00051 115.26351 96.70953 94.93277 113.93927 111.13326 86.22489
[46] 85.85010 107.29164 115.37066 97.75308 117.62215 107.96212 87.75947 106.82239 77.41274
[55] 128.66047 139.60800 92.65557 79.11731 111.39439 97.29891 148.03236 99.21520 113.79479
[64] 100.56004 85.13454 103.77585 63.90083 129.31110 103.06507 143.45223 109.51019 85.80107
[73] 112.21453 81.31805 74.92733 105.82892 91.13416 100.02211 101.48683 88.20958 88.62663
[82] 97.29643 123.56174 69.52866 111.87892 106.65901 121.26200 93.91632 107.40038 105.34198
[91] 89.14960 124.15736 123.20805 114.00427 131.73667 111.16973 74.46816 88.53469 75.50775
[100] 90.53199
Then we can add 10 to each element of the vector like this:
> normal1<-normal+10
And we can visualize the results like this
> normal1
[1] 97.47092 113.67287 93.28743 141.90562 116.59016 93.59063 119.74858 124.76649 121.51563
[10] 103.89223 140.23562 117.79686 97.57519 65.70600 132.49862 109.10133 109.67619 128.87672
[19] 126.42442 121.87803 128.37955 125.64273 111.49130 70.21297 122.39651 108.87743 106.88409
[28] 80.58495 100.43700 118.35883 137.17359 107.94425 117.75343 108.92390 82.45881 101.70011
[37] 102.11420 108.81373 132.00051 125.26351 106.70953 104.93277 123.93927 121.13326 96.22489
[46] 95.85010 117.29164 125.37066 107.75308 127.62215 117.96212 97.75947 116.82239 87.41274
[55] 138.66047 149.60800 102.65557 89.11731 121.39439 107.29891 158.03236 109.21520 123.79479
[64] 110.56004 95.13454 113.77585 73.90083 139.31110 113.06507 153.45223 119.51019 95.80107
[73] 122.21453 91.31805 84.92733 115.82892 101.13416 110.02211 111.48683 98.20958 98.62663
[82] 107.29643 133.56174 79.52866 121.87892 116.65901 131.26200 103.91632 117.40038 115.34198
[91] 99.14960 134.15736 133.20805 124.00427 141.73667 121.16973 84.46816 98.53469 85.50775
[100] 100.53199
The sample mean is given by:
And the sample deviation by:
If we want to calculate the mean and standard deviation for the original data we can do this:
> mean(normal)
[1] 102.1777
And the standard deviation with:
> sd(normal)
[1] 17.96399
Other way to calculate the deviation is:
> sqrt(sum((normal-mean(normal))^2/(length(normal)-1)))
[1] 17.96399
