Use the following sample data to fond the standard deviation: -1, 0, 2, 3, 7, 10, 10?

1 Answer
May 11, 2018

Approx. #4.23#

Explanation:

First of all, we need the mean: sum of all values, divided by how many values we have

#\mu = \frac{-1+0+2+3+7+10+10}{7} \approx 4.43#

Then, we need the squared distances of each element from the mean, i.e. for each value #x#, we need to compute #(x-\mu)^2#

#(-1-4.43)^2 \approx 29.48#
#(0-4.43)^2 \approx 19.62#
#(2-4.43)^2 \approx 5.90#
#(3-4.43)^2 \approx 2.04#
#(7-4.43)^2 \approx 6.60#
#(10-4.43)^2 \approx 31.02#
#(10-4.43)^2 \approx 31.02#

Now sum all the squared distances, and divide them by the number of observations to obtain the variance:

#\sigma^2 = \frac{29.48+19.62+5.90+2.04+6.60+31.02+31.02}{7}=\frac{125.68}{7} \approx 17.95#

Finally, the standard deviation is defined as the square root of the variance:

#\sigma = \sqrt{\sigma^2} = \sqrt{17.95} \approx 4.23#