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We are asked to find the standard deviation of the data: 12,8,11,10,7,10,15,13,14,9
1) If you assume that this is the population, the formula is:
`sigma = sqrt( (sum(X-mu)^2)/N)` where `sigma` is the standard deviation, `mu` is the mean (arithmetic mean) of the data, and `N` the number of data elements in the set. Calculating the mean we get `mu=10.9` .
Since there are 10 elements, we have:
2) If the data is a sample we use `s=sqrt((sum(X-bar(X))^2)/(n-1))`
` ` where `s` is the sample standard deviation, `bar(X)` is the sample mean, and `n` is the number of data elements.
Alternatively, we can use the shortcut formula
We have `sumX=109,sumX^2=1249,n=10` so:
Since neither answer appears, the correct choice is (d) none.
d.) none of the above
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