Statistics Short Questions (Question 3 & 4)


Question 3:
The mean of five numbers is p . The sum of the squares of the numbers is 120 and the standard deviation is 2q. Express p in terms of q.

Solution:
Mean  x ¯ = x N p = x 5 x=5 p Standard deviation, σ= x 2 N x ¯ 2 2q= 120 5 ( p ) 2 4 q 2 =24p p=244 q 2



Question 4:
A set of positive integers consists of 1, 4 and p. The variance for this set of integers is 6. Find the value of p.

Solution:
Variance,  σ 2 = x 2 N x ¯ 2 6= 1 2 + 4 2 + p 2 3 ( 1+4+p 3 ) 2 6= 17+ p 2 3 ( 5+p 3 ) 2 6= 17+ p 2 3 [ 25+10p+ p 2 9 ] 6= 51+3 p 2 2510p p 2 9 2 p 2 10p+26=54 2 p 2 10p+28=0 p 2 5p+14=0 ( p7 )( p+2 )=0 p=2 (not accepted) p=7