# Easy Stats

• Jun 7th 2013, 09:37 AM
Tutu
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
• Jun 7th 2013, 09:37 AM
Tutu
Re: Easy Stats
Sorry, given that p<q!
Thank you so much in advance!
• Jun 7th 2013, 08:31 PM
ibdutt
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. Attachment 28546
• Jun 7th 2013, 09:24 PM
Tutu
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...
• Jun 7th 2013, 10:06 PM
ibdutt
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
• Jun 7th 2013, 10:29 PM
ibdutt
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
• Jun 7th 2013, 10:39 PM
Tutu
Re: Easy Stats
Yes, there was a mistake in my working. Thank you so so so much, really!!
• Jun 7th 2013, 11:46 PM
Tutu
Re: Easy Stats
Yes, there was a mistake in my working. Thank you so so so much, really!!