Mean Deviation about Mean for Continuous Frequency Distributions

Q. 95-105 105-115 115-125 125-135 135-145 145-15510. Height9in cmsNumber ofboys1326301210

Q. 9. Income per 0-100 100-200 200-300 300-400 400-500 500-600 600-700 700-800day inNumber 4 8of persons104

Q. Express the following expression in the form of $a+ib:\frac{(3+i\sqrt{5})(3-i\sqrt{5})}{(\sqrt{3}+\sqrt{2}i)-(\sqrt{3}-i\sqrt{2})}$

Q. In a class of $60$ students, $30$ opted for NCC, $32$ opted for NSS and $24$ opted for both NCC and NSS. If one of these students is selected at random, find the probability that
(i) The student opted for NCC or NSS
(ii) The student has opted neither NCC nor NSS
(iii) The student has opted NSS but not NCC

Q. If A and G be A.M. and G.M., respectively between two positive numbers prove that the numbers are $A\pm \sqrt{(A+G)(A-G)}.$

Q. The scores of batsmen(S) in a cricket series is tabulated below. The mean deviation about mean for the scores is
$\begin{array}{ccccccc}S& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60\\ f_i& 12& 18& 27& 20& 17& 6\end{array}$

1. 15
2. 99
3. 10
4. 50

Q.

The mid - points of class intervals $x_i$ along with respective frequencies $f_i$ for recorded observations are given. Calculate the mean deviations about mean $x$

1. $\frac{1}{N}{\sum }_{i=1}^n{f}_i|x_i-\overline{x}|whereN={\sum }_{i=1}^n{f}_i$

2. ${\sum }_{i=1}^n{f}_i|x_i-\overline{x}|whereN={\sum }_{i=1}^n{f}_i$

3. $\frac{1}{N}{\sum }_{i=1}^n{f}_i|x_i+\overline{x}|whereN={\sum }_{i=1}^n{f}_i$

4. $\frac{1}{N}{\sum }_{i=1}^n=f_i|\overline{x}|whereN={\sum }_{i=1}^n{f}_i$

Q. The ratio of the A.M. and G.M. of two positive numbers $a$ and $b$, is $m:n$. Show that $a:b=(m+\sqrt{m^2-n^2}):(m-\sqrt{m^2-n^2})$