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