The standard deviation of 1,2,3,....25 is?

1 Answer
Anjali G
May 24, 2018

The standard deviation is #sigma = 7.2111#. This is the population standard deviation, not the sample standard deviation. (The difference is explained here).

Explanation:

I did this by writing a formula into a spreadsheet to find the standard deviation of the integers from 1 to 25.

Alternatively, we could calculate it by hand - click here for details.

#"Standard deviation " sigma = sqrt(frac{sum_(i=1)^(N)(x_i - mu)^2}{N})#

We know the mean of the dataset is:
#mu = frac{sum_(i=1)^25 (i)}{25} = frac{1 + 2 + 3 + ... +25}{25}#

#mu = frac{1+25}{2} = 13#

Substitute values:
#sigma = sqrt(frac{sum_(i=1)^(25)(x_i - 13)^2}{25})#

# sigma= sqrt(frac{(1-13)^2+(2-13)^2+(3-13)^2 + ... + (25-13)^2}{25})#

#sigma = sqrt(frac{12^2+11^2 + ... +2^2+1^2+0^2+1^2 + ... + 11^2+12^2}{25})#

#sigma = sqrt(1300/25) = sqrt52#

#sigma = 7.2111#

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