Hi I really hope someone can help me here, I really am stuck and would like to know how to do them! 1.) A sample of 8 integers has a mean of 5 and a variance of 5.25. The integers are 1,3,5,7,4,5,p,q. Find p and q given that p

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- Jun 7th 2013, 08:37 AMTutuEasy Stats
Hi I really hope someone can help me here, I really am stuck and would like to know how to do them! 1.) A sample of 8 integers has a mean of 5 and a variance of 5.25. The integers are 1,3,5,7,4,5,p,q. Find p and q given that p

- Jun 7th 2013, 08:37 AMTutuRe: Easy Stats
Sorry, given that p<q!

Thank you so much in advance! - Jun 7th 2013, 07:31 PMibduttRe: Easy Stats
Use first the definition of mean, that will give p = q = 15.

Then we are given variance I

Use the formula attached to find variance. now you will have two equations in two variables just solve the equations to get p and q. Attachment 28546 - Jun 7th 2013, 08:24 PMTutuRe: Easy Stats
Hi thanks for the reply! that's what I did. Ended up with 2 equations, p^2+q^2-10p-10q = -8 and p+q = 15. Got stuck there...

- Jun 7th 2013, 09:06 PMibduttRe: Easy Stats
Remember a^2 +b^2 = ( a + b)^2 - 2ab

Also we can write - 10 p -10 q = -10 ( p + q )

Plu in th value of p + q - Jun 7th 2013, 09:29 PMibduttRe: Easy Stats
There appears to be something wrong in your equation.

From variance equation you should get

p^2 + q^2 - 10(p+q) = -33

OR (p+q)^2 - 2pq -10 (p+q) = -33

(15)^2 - 2pq -150 = -33

225 -2pq - 150 = -33

2pq = 108 OR pq = 54

Now u have. Two equations

P + q = 15 and pq = 54

Solve the see and you will get two values of p as 9 and 6

since p < q select p = 6 And q will be 9 - Jun 7th 2013, 09:39 PMTutuRe: Easy Stats
Yes, there was a mistake in my working. Thank you so so so much, really!!

- Jun 7th 2013, 10:46 PMTutuRe: Easy Stats
Yes, there was a mistake in my working. Thank you so so so much, really!!