Q22. Find the mean of 1,3,5,....., 2n-1.
Ans:
Hint:
You can see $\small u_{1}=1[2\times 1-1], u_{2}=3[2\times 2-1], u_{3}=5[2\times 3-1],....,u_{n}=2\times n-1$. As general let think about $\small u_{i}=2i-1$.
Now the mean, $\small \bar u$=$\small \frac{\sum_{i=1}^{n} u_{i}}{n}$=$\small \frac{\sum_{i=1}^{n} (2i-1)}{n}$=$\small \frac{2\sum_{i=1}^{n} i-n}{n}$=$\small \frac{2(1+2+...+n)-n}{n}$]
Ans: $\small n$
Q23.
Q24. Practical Problem.
Q25. Find the harmonic mean of the reciprocals of the values 2,3,...10 with equal frequencies.
Ans:
Hint: Let $\small x_{1}$= $\small =\frac{1}{2}, x_{2}= \frac{1}{3},...,x_{10}=\frac{1}{10}$. Put the values in the formula of $\small H.M$.=$\small \frac{9}{2+3+4+....+10}$.
Q26. The variables $\small x$ and $\small u$ are related as $\small x=1.5u+2.5$ and $\small u$ has median 20. calculate the median of x.
Ans:
Hint: $\small Median(x)=1.5 Median(u)+2.5$
Q27. Parctical Problem
Q28. Parctical Problem
Q29. Parctical Problem
Q30. If the relation between two variables $\small x$ and $\small y$ is $\small 2x+3y=7$ and the mode of y is 2, find the mode of x.
Hint: $\small 2 Mode(x)+ 3 Mode(y)=7$
Q31. If $\small 3u=x$ and the harmonic mean of $\small x$ is 0.09.Find the harmonic mean of s$\small u$.
Hint: $\small H.M(x)$ be the harmonic mean of $\small x$. Let, $\small u=ax$ then $\small H.M(u)= a H.M(x)$.
Q32. If both $\small x$ and $\small y$ assumes positive values only and $\small y=3x^2$, then establish a relation between geometric mean of $\small y$ that of $\small x$.
Ans: $\small G.M(x)$ be the geometric mean of $\small x$. Let, $\small y=3x^2$ then
$\small G.M(y)$
=$\small [3^n (x_{1}x_{2}......x_{n})^2]^\frac{1}{n}$
=$\small [3(G.M(y)^2]$
Q33.Practical Problem
Part-5
Tags: Measures of Central Tendency(Part-4)| Giri Banarjee Statistics Solution| Problems on Mean