## Find a population data set that contains 6 entries has a mea

Standard deviation, mean, variance, z-scores, t-tests, etc.
nicknation
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### Find a population data set that contains 6 entries has a mea

Find a population data set that contains 6 entries has a mean of 5 and has a standard deviation of 2.
??????

stapel_eliz
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If the six entries have a mean of 5, what then must be their sum?

Square the standard deviation to get the value of the variance, and then use the alternative formula displayed here. From the first calculation above, you can substitute for the sum of the values xi. Using this, you can solve for the value of the sum of the squares.

Now pick values that have the appropriate sum, and see what is the sum of their squares. Make adjustments, as necessary, until you arrive at a set of values which works. (I believe there can be more than one "right" answer to this exercise.)

nicknation
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### Re: Find a population data set that contains 6 entries has a mea

sum=30
var=4
i dont understand how 2 use formula???

nona.m.nona
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### Re: Find a population data set that contains 6 entries has a mea

Plug into the formula:

$\sigma^2 = \frac{\sum X^2 - \frac{(\sum X)^2}{N}}{N}$

$4 = \frac{\sum X^2 - \frac{900}{6}}{6}$

$24 = \sum X^2 - 150$

$174 = \sum X^2$

So find 6 numbers that add up to 30, and see what the sum of their squares is. Then make adjustments, if necessary.

I hope that makes sense.

nicknation
Posts: 23
Joined: Wed Mar 11, 2009 3:28 pm

### Re: Find a population data set that contains 6 entries has a mea

i did 3,4,4,5,6,8=30
but 9+16+16+25+36+64=165
wat now?

stapel_eliz
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Now you make the adjustments mentioned earlier.

Your sum is correct, but the sum of the squares is too small. Can you adjust the values for the sum to move the sum of the squares in the right direction? For instance, what happens if you change the 3 to a 2? You'd need to adjust one of the other numbers to be one larger. Pick one, and see what happens to your sum of squares.

(Keep trying adjustments of this sort until you find a set of values which works. There is no "formula" for this part, as near as I can figure. You just have to allow yourself some time to fiddle with the numbers.)

nicknation
Posts: 23
Joined: Wed Mar 11, 2009 3:28 pm

### Re: Find a population data set that contains 6 entries has a mea

if i do the 3 to 2 and the 6 to 7 the sum is rite
so ans is 2,4,4,5,7,8???

stapel_eliz
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Joined: Mon Dec 08, 2008 4:22 pm
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That is one solution. There may be more. Any set of numbers which fulfills the requirements should be acceptable.