Algebra 2 (measures of central tendency and variation)

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Find the variation and standard deviation.

1.) {7,4,3,9,2}=

2.) {35,67,21,16,24,51,18,32}=

3.) {19,23,17,20,25,19,15,22}=

4.) {5,12,10,13,8,11,15,12}=

Oct 23rd, 2017

Ok, so variance is just the standard deviation squared. If you have a graphing calculator, message me and I can tell you how it will automatically find it for you. 

But anyways:

When you want the standard deviation you need to find the variance. To find the variance you need the mean. To calculate the mean, you add up each number in the data set, and then divide it by how many numbers are in the data set. So for example: 7+4+3+9+2=25. And 25 / 5 (divided by 5) = 5. So the mean (or average, whichever suits you best) is 5. 

Now that we have the mean, you need to find the variance. The variance, is like the average square distance each number in the data set is away from the mean. So again, for example: 7-5=2 and 4-5=-1 (but the negatives don't really matter much, because these numbers will be squared). 3-5=-2. 9-5=4 and 2-5=-3 

So the numbers we have are: -3, 4, -2, -1, 2. We are going to square each of these: (-3)^2 (which is the same as saying -3 "squared" or "to the power of 2") is 9. 4 squared is 16. -2 squared is 4. -1 squared is 1. 2 squared is 4. 

We now have a new data set. : 9, 16, 4, 1, 4. We are going to add these and find the average. 9+16+4+1+4= 34. Then you divide by how many numbers are in this data set. You get: 34/5. Which as a decimal is 6.8. This number is your variance. 
The standard deviation is just the square root of your variance. (this also means that in a given situation where you don't have variance, and you only have the standard deviation, and you get a problem that says to find the variance, you would square the standard deviation b/c if the standard deviation is the square root of the variance, then the variance is equal to the standard deviation squared).  When you take the square root of 6.8 you get 2.6076 which we'll just round to 2.608. 

So for the first problem, your answers are:

Variance= 6.8

Standard Deviation=2.608.

Hope this helps. Let me know if you need help with anything else. Just message me. Take care kiddo. 

-Doctor Turner

Feb 3rd, 2015

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