SOLUTION: The heights of 10 randomly selected fourth grade boys are (in inches) are 53, 53, 54, 56, 56, 56, 50, 57, 59, and 56. Find the sample standard deviations to 2 decimal places. 2.67

Question 984219: The heights of 10 randomly selected fourth grade boys are (in inches) are 53, 53, 54, 56, 56, 56, 50, 57, 59, and 56. Find the sample standard deviations to 2 decimal places.
2.67
2.54
3.54
2.56
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 = (53+53+54+56+56+56+50+57+59+56)/10 = 550/10 = 55

So the sample mean is xbar = 55

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

Now subtract the sample mean from EVERY data value:

53-55 = -2
53-55 = -2
54-55 = -1
56-55 = 1
56-55 = 1
56-55 = 1
50-55 = -5
57-55 = 2
59-55 = 4
56-55 = 1

So the differences are: -2, -2, -1, 1, 1, 1, -5, 2, 4, 1

Now square each difference:

(-2)^2 = 4
(-2)^2 = 4
(-1)^2 = 1
(1)^2 = 1
(1)^2 = 1
(1)^2 = 1
(-5)^2 = 25
(2)^2 = 4
(4)^2 = 16
(1)^2 = 1

Now add up each square:

4+4+1+1+1+1+25+4+16+1 = 58

Now divide that sum by n-1 = 10-1 = 9 to get 58/9 = 6.44444444444444

So the sample variance is 6.44444444444444

Finally, take the square root of 6.44444444444444 to get 2.53859103528797

So the sample standard deviation is 2.53859103528797 which rounds to 2.54

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