Question

PLEASE HELP MEEEEEE!!

Answer 1

To compute the standard deviation, we first need the array of distances from the mean. So, we consider the difference between each element of the dataset and the mean:

$20-22, 12-22, 27-22, 23-22, 18-22, 20-22, 30-22, 26-22$

which is

$-2, 10, 5, 1, -4, -2, 8, 4$

Then, we need to square this array:

$4, 100, 25, 1, 16, 4, 64, 16$

Then, we consider the mean of this new array, so we sum its components and divide by the number of elements:

$\dfrac{4+ 100+ 25+ 1+ 16+4+ 64+ 16}{8} = \dfrac{230}{8} = \dfrac{115}{4}$

This is the variance, i.e. the standard deviation squared. So, we only need to take the square root of the variance to get the standard deviation:

$\sigma = \sqrt{\dfrac{115}{4}} = \dfrac{\sqrt{115}}{2} \approx 5.36$