# The standard deviation of 12, 8, 11, 10, 7, 10, 15, 13, 14, 9 is__ a.) 2.88 b.) 3.66 c.) 2.01 d.) none of the above

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### 2 Answers

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` .

Now `sum(X-mu)^2=(12-10.9)^2+(8-10.9)^2+...+(9-10.9)^2`

`=1.21+8.41+.01+.81+15.21+.81+16.81+4.41+9.61+3.61=60.9`

Since there are 10 elements, we have:

`sigma=sqrt(60.9/10)~~2.47`

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

`s=sqrt((n(sum X^2)-(sumX)^2)/(n(n-1)))`

We have `sumX=109,sumX^2=1249,n=10` so:

`s=sqrt((10(1249)-109^2)/(10(9)))=sqrt(609/90)~~2.60`

**Since neither answer appears, the correct choice is (d) none.**

d.) none of the above