SOLUTION: 16, 5, 18, 9, 11 Calculate the standard deviation (to the nearest hundredth)

Question 703724: 16, 5, 18, 9, 11
Calculate the standard deviation (to the nearest hundredth)

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First, we need to find the sample mean xbar

xbar = (16+5+18+9+11)/5 = 59/5 = 11.8

So the sample mean is xbar = 11.8

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

Now subtract the sample mean from EVERY data value:

16-11.8 = 4.2
5-11.8 = -6.8
18-11.8 = 6.2
9-11.8 = -2.8
11-11.8 = -0.8

So the differences are: 4.2, -6.8, 6.2, -2.8, -0.8

Now square each difference:

(4.2)^2 = 17.64
(-6.8)^2 = 46.24
(6.2)^2 = 38.44
(-2.8)^2 = 7.84
(-0.8)^2 = 0.64

Now add up each square:

17.64+46.24+38.44+7.84+0.64 = 110.8

Now divide that sum by n-1 = 5-1 = 4 to get 110.8/4 = 27.7

So the sample variance is 27.7

Finally, take the square root of 27.7 to get 5.26307894677631

So the sample standard deviation is 5.26307894677631 which rounds to the nearest hundredth to get 5.26

So the answer is 5.26

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