SOLUTION: Use the formula and show your work for finding the sample standard deviation and variance of the scores on a test:
65,88,83,80,78,90
n
√(1/(n-1) Σ (xᵢ-x̄)^2)
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-> SOLUTION: Use the formula and show your work for finding the sample standard deviation and variance of the scores on a test:
65,88,83,80,78,90
n
√(1/(n-1) Σ (xᵢ-x̄)^2)
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Question 1178333: Use the formula and show your work for finding the sample standard deviation and variance of the scores on a test:
65,88,83,80,78,90
n
√(1/(n-1) Σ (xᵢ-x̄)^2)
i=1
I'm not sure how the formatting is going to come out but the sigma is supposed to look like:
n
Σ
i=1
Make this list:
i xi
---------------
1 65
2 88
3 83
4 80
5 78
6 90
Find the mean (the average of those 6 number which is 80 2/3
Then you subtract the mean, x̄ = 80 2/3 from each one, and put them in a list
out to the right:
i xi xi-x̄
---------------
1 65 -15 2/3
2 88 7 1/3
3 83 2 1/3
4 80 - 2/3
5 78 -2 2/3
6 90 9 1/3
--------------
Then you square each number in that list and put them in a list out to the
right:
i xi xi-x̄ (xi-x̄)²
------------------------
1 65 -15 2/3 245 4/9
2 88 7 1/3 53 7/9
3 83 2 1/3 5 4/9
4 80 - 2/3 4/9
5 78 -2 2/3 7 1/9
6 90 9 1/3 87 1/9
-------------------------
484 0 399 1/3
÷ ÷
6 5 <--divide by 1 less than the number of numbers.
= =
80 2/3 79 13/15
= =
x̄ σ² = the variance of the sample
To get the standard deviation, we take the square root of the variance:
<--standard deviation
Edwin
