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 2 q = 120 5 ( p ) 2 4 q 2 = 24 p p = 24 4 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 + 10 p + p 2 9 ] 6 = 51 + 3 p 2 25 10 p p 2 9 2 p 2 10 p + 26 = 54 2 p 2 10 p + 28 = 0 p 2 5 p + 14 = 0 ( p 7 ) ( p + 2 ) = 0 p = 2  (not accepted) p = 7

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