Question 984219
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 <font color="red">2.54</font>