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