Question 771309: What is the variance of the set of numbers? Please show work
16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 22, 22, 23, 23, 23, 24, 24, 24, 24, 24, 25, 25, 25, 25, 25, 25, 25, 25, 26, 26, 26, 27, 27, 27, 27, 27, 27, 28, 28, 28, 28, 28, 28, 29, 29, 29, 29, 30, 30, 31, 32, 32, 32, 33, 34, 34, 34, 34, 34, 33, 35, 35, 35, 35, 35, 36, 36, 37, 37, 38, 38, 39, 40, 41, 42, 42, 42, 42, 42, 43, 44, 45, 46, 48, 49, 51, 53, 55, 55, 56, 58, 60, 62
Thanks!
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website!
You'll have to do it for your long list of data.
This one stops at 19, but yours goes to 62.
I'm just going to show you how you would do it
if there were only the first 4 values in your
list. So don't use the sums below. Do it for
you whole list, which will take a long time.
Make this chart. The frequencies f are how many of that number
are in the list. You have 2 16s, 4 17's, 5 18's and 6 19's.
Then multiply the f's by the x's. And add up the f's and the
f·x's.
x f f·x x-x (x-x)² f·(x-x)²
----------------------------------
16 2 32
17 4 68
18 5 90
19 6 114
---------------------------------
17 304
Now divide the ∑f·x = 304 by the ∑f = n = 17 and get x = 17.88
Subtract x = 17.88 from each x and put it in the next column.
x f f·x x-x (x-x)² f·(x-x)²
----------------------------------
16 2 32 -1.88
17 4 68 -.88
18 5 90 .12
19 6 114 1.12
---------------------------------
17 304
We square each number in that column
and put it in the next column.
x f f·x x-x (x-x)² f·(x-x)²
----------------------------------
16 2 32 -1.88 3.53
17 4 68 -.88 .77
18 5 90 .12 1.44
19 6 114 1.12 1.25
---------------------------------
17 304
Now we multiply the number in column f times
the numbers in column (x-x)² and put those
values in the last column. Add that last column
x f f·x x-x (x-x)² f·(x-x)²
----------------------------------
16 2 32 -1.88 3.54 7.09
17 4 68 -.88 .77 3.11
18 5 90 .12 .01 .07
19 6 114 1.12 1.25 7.49
---------------------------------
17 304 17.76
Now divide that ∑f·(x-x)² by n-1 which is 17-1 or 16,
and you get the variance = s² = 1.11
You'll have to do that will all your data. It's
going to be a lot of work. And maybe you'll need
to take the decimals out further to get the
accuracy you need.
Edwin
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