Question

Find the standard deviation. 44, 46, 33, 10, 50, 27

Answer 1

First, find the mean:

(44 + 46 + 33 + 10 + 50 + 27) / 6

210/6

35

mean = 35

 

Now, find the variance:

Variance = Average of squared differences from the mean

Start with (44, 46, 33, 10, 50, 27)

Now subtract the mean (35) from each number, giving us (9, 11, -2, -25, 15, -8).  That's the differences from the mean.

Now square those, giving us (81, 121, 4, 625, 225, 64).  That's the squared differences from the mean.

Now average those: (81 + 121 + 4 + 625 + 225 + 64) / 6 = 1120/6 = 186.67

(approximate, actual value is 186.66666, with 6's forever)

Variance = 186.67  

 

Standard deviation = square root of the variance

SD = sqrt(186.67)

SD = 13.66