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How to find mean and standard deviation from frequency table in R?
To find the mean and standard deviation from frequency table, we would need to apply the formula for mean and standard deviation for frequency data. For example, if we have a data frame called df that contains a column x for units and frequency for counts then the mean and standard deviation can be calculated as −
Mean = sum(df$x*df$frequency)/sum(df$frequency) SD = sqrt(sum((df$x−Mean)**2*df$frequency)/(sum(df$frequency)−1)) respectively.
Example1
x<−rpois(20,5) frequency<−sample(1:100,20) df1<−data.frame(x,frequency) df1
Output
x frequency 1 6 4 2 7 26 3 1 86 4 2 6 5 4 52 6 4 61 7 1 55 8 4 23 9 8 38 10 3 40 11 8 54 12 10 56 13 7 74 14 9 70 15 7 59 16 16 95 17 4 20 18 5 9 19 4 82 20 9 45
Example
Mean=sum(df1$x*df1$frequency)/sum(df1$frequency) Mean
Output
[1] 6.55288
Example
SD=sqrt(sum((df1$x−Mean)**2*df1$frequency)/(sum(df1$frequency)−1)) SD
Output
[1] 4.172396
Example2
y<−rnorm(20,25,3.24) frequency<−rpois(20,10) df2<−data.frame(y,frequency) df2
Output
y frequency 1 27.44960 7 2 25.80343 5 3 22.64088 8 4 22.39061 7 5 24.55087 7 6 24.41826 16 7 23.24647 11 8 25.61511 9 9 22.42244 11 10 26.77522 14 11 21.89209 11 12 22.95852 8 13 25.79808 16 14 22.39654 6 15 21.20728 12 16 28.25911 17 17 26.67983 8 18 25.24964 12 19 20.92070 8 20 28.25806 7
Example
Mean=sum(df2$y*df2$frequency)/sum(df2$frequency) Mean
Output
[1] 24.58724
Example
SD=sqrt(sum((df2$y−Mean)**2*df2$frequency)/(sum(df2$frequency)−1)) SD
Output
[1] 2.284964
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