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 ˉx=xNp=x5x=5pStandard deviation, σ=x2Nˉx22q=1205(p)24q2=24pp=244q2



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, σ2=x2Nˉx26=12+42+p23(1+4+p3)26=17+p23(5+p3)26=17+p23[25+10p+p29]6=51+3p22510pp292p210p+26=542p210p+28=0p25p+14=0(p7)(p+2)=0p=2 (not accepted)