I need help I really don’t understand

Question

Find the population standard deviation of the following data (build the table). 84, 72, 89, 85, 99, 81

Answer 1

Here are the formulas:

deviation = stat - mean <-- deviation is the distance between the stat and the mean

population variance = SUM of deviations squared / N where N=5 stats <-- this is the DEFINITION formula

shortcut formula for variance = [Sum of (stats^2) - N* mean^2]/N

population standard deviation is the square root of the variance

(NOTE: if we were given a SAMPLE, we divide by N-1 instead of N)

Next note that the total of the stats is 426, so then the mean is 426/5 = 85.2

SET UP A TABLE LIKE THIS, Leaving a row for the totals:

x deviation devation^2 X^2

72 -13.2 174.24 5184

89 3.8 14.44 7921

85 -0.2 0.04 7225

99 13.8 190.44 9801

81 -4.2 17.64 6561

----------------------------------------------------------------

totals 426 0 396.8 36692

For example, for stat x=72, the deviation is 72-85.2 = -13.2

You can verify the rest of the table

The sum of the deviations MUST BE ZERO!!!!

The numerator of the shortcut formula says: 36692 - 5*85.2^2 = 396.8, which

agrees with the total of the deviations squared.

population variance = 396.8/5 = 79.36

population standard deviation is the square root of that, which is