1. ## Easy 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

2. ## Re: Easy Stats

Sorry, given that p<q!
Thank you so much in advance!

3. ## Re: 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.

4. ## Re: 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...

5. ## Re: 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

6. ## Re: 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

7. ## Re: Easy Stats

Yes, there was a mistake in my working. Thank you so so so much, really!!

8. ## Re: Easy Stats

Yes, there was a mistake in my working. Thank you so so so much, really!!