SOLUTION: Need help with this problem: Find the rand,standard deviation,and variance for the following sample data: 77,67,5,30,19,79,9,23,1,51,56,82,27,1,9,90 not really sure how to do any p

Question 476935: Need help with this problem: Find the rand,standard deviation,and variance for the following sample data: 77,67,5,30,19,79,9,23,1,51,56,82,27,1,9,90 not really sure how to do any part of this need step by step if at all possible please and thank you!!!!!!!!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Not familiar with the term "rand". Is that a typo?

Finding the sample standard deviation:

First, we need to find the sample mean xbar

xbar = (77+67+5+30+19+79+9+23+1+51+56+82+27+1+9+90)/16 = 626/16 = 39.125

So the sample mean is xbar = 39.125

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

Now subtract the sample mean from EVERY data value:
77-39.125 = 37.875
67-39.125 = 27.875
5-39.125 = -34.125
30-39.125 = -9.125
19-39.125 = -20.125
79-39.125 = 39.875
9-39.125 = -30.125
23-39.125 = -16.125
1-39.125 = -38.125
51-39.125 = 11.875
56-39.125 = 16.875
82-39.125 = 42.875
27-39.125 = -12.125
1-39.125 = -38.125
9-39.125 = -30.125
90-39.125 = 50.875

So the differences are: 37.875, 27.875, -34.125, -9.125, -20.125, 39.875, -30.125, -16.125, -38.125, 11.875, 16.875, 42.875, -12.125, -38.125, -30.125, 50.875

Now square each difference:
(37.875)^2 = 1434.515625
(27.875)^2 = 777.015625
(-34.125)^2 = 1164.515625
(-9.125)^2 = 83.265625
(-20.125)^2 = 405.015625
(39.875)^2 = 1590.015625
(-30.125)^2 = 907.515625
(-16.125)^2 = 260.015625
(-38.125)^2 = 1453.515625
(11.875)^2 = 141.015625
(16.875)^2 = 284.765625
(42.875)^2 = 1838.265625
(-12.125)^2 = 147.015625
(-38.125)^2 = 1453.515625
(-30.125)^2 = 907.515625
(50.875)^2 = 2588.265625

Now add up each square:
1434.515625+777.015625+1164.515625+83.265625+405.015625+1590.015625+907.515625+260.015625+1453.515625+141.015625+284.765625+1838.265625+147.015625+1453.515625+907.515625+2588.265625 = 15435.75

Now divide that sum by n-1 = 16-1 = 15 to get 15435.75/15 = 1029.05

Finally, take the square root of 1029.05 to get 32.0788092048318

So the sample standard deviation is 32.0788092048318

Now simply square this value to get the sample variance (32.0788092048318)^2 = 1029.05

So the sample variance is 1029.05
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