Q8. What do you mean by weighted mean? State their uses?
Ans: Follow standard books.
Q9. Compare mean, median, mode as measures of central tendency.
Ans:
Q10. How are the different averages of a variable affected if each of the variable is doubled?
Ans: [Hint: \small \bar x is the mean of variable then find the mean of \small y=2x]
Q11.If the values of a variable are in G.P, then prove that A.M,G.M,H.M of the values are also in G.P.
Ans:
[Hint: The observations are \small a, ar, ar^2, ar^3, ....., ar^(n-1), G.M= \small ar^{\frac{n-1}{2}}, H.M=\small \frac{anr^n(1-r)}{r(1-r^n)}, A.M=\small \frac{a(r^n-1)}{n(r-1)}]
Q12. A variable assumes two distinct values 0 and 1. Of the total number n of the observations, the value 1 occurs \small np times, while the value 0 occurs \small nq times.Calculate the mean of the observations.
[\small Hint: \small x_{1}=1, x_{2}=0, \small f_{1}=np, f_{2}=nq,\small \sum_{i=1}^{2} f_{i}=f_{1}+f_{2}=n(p+q)=n,\small \bar x=\small \frac{\sum_{i=1}^{2} x_{i}f_{i}}{\sum_{i=1}^{2}f_{i}}]
Q13.If the geometric mean of \small n_{1} values of a variable \small x be \small g_{1} and that of another \small n_{2} values be \small g_{2}, then find the geometric mean of the combined data in terms of \small g_{1} and \small g_{2}.
Ans:
[Hint:
Q14.If A.M and G.M of two positive real numbers are 25 and 15 respectively, then find their H.M.
[Hint: \small \frac{x_{1}+x_{2}}{2}=25, \small \sqrt(x_{1}x_{2})=15, Find \small x_{1},x_{2},H.M]
Tags: Measures of Central Tendency(Part-2)| Giri Banarjee Statistics Solution| Problems on Mean