Question 941944: The following data represent the number of children in a sample of 10 families from Chicago: 4, 2, 1, 1, 5, 3, 0, 1, 0, and 2.
Compute the variance of the data. Place your answer, rounded to two decimal places, in the blank.
Answer by Edwin McCravy(20064)   (Show Source):
You can put this solution on YOUR website!
We write them in a column headed x and we add them, then divide
that sum by the number of numbers which is 10
x
-----------------------------
4
2
1
1
5
3
0
1
0
2
---
10)19
---
1.9 = x
Now we make a column out to the right of that one headed x-x
and subtract 1.9 from every number in the first column:
_
x x-x
-----------------------------
4 2.1
2 0.1
1 -0.9
1 -0.9
5 3.1
3 1.1
0 -1.9
1 -0.9
0 -1.9
2 0.1
---
10)19
---
1.9 = x
To the right of that, we make a column with the heading (x-x)²,
and we square every number in the previous column. Then we
add that column, divide by 1 lees than 10, which is 9:
_ _
x x-x (x-x)²
-----------------------------
4 2.1 4.41
2 0.1 0.01
1 -0.9 0.81
1 -0.9 0.81
5 3.1 9.61
3 1.1 1.21
0 -1.9 3.61
1 -0.9 0.81
0 -1.9 3.61
2 0.1 0.01
--- -----
10)19 9)24.90
--- _ -----
1.9 = x 2.76666667 = s² = variance
Rounded to two decimal places, the variance is 2.77
Edwin
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