Approach to Find Mean for Frequency Distribution Table

Q. Question 4
In the formula $\overline{x}=a+h\left(\frac{\sum f_i{u}_i}{\sum f_i}\right),$ for finding the mean of grouped frequency distribution $u_i$ is equal to
(a) $\frac{x_i+a}{h}$
(b) $x_i+a$
(c) $\frac{x_i+a}{h}$
(a) $\frac{a-x_i}{h}$

Q.

Find the missing frequencies in the following frequency distribution whose mean is 34.
$\begin{array}{cccccccc}\text{x}& 10& 20& 30& 40& 50& 60& \text{Total}\\ \text{f}& 4& f_1& 8& f_2& 3& 4& 35\end{array}$

Q.

Find the missing frequencies in the following frequency distribution whose mean is 34.
$\begin{array}{cccccccc}\text{x}& 10& 20& 30& 40& 50& 60& \text{Total}\\ \text{f}& 4& f_1& 8& f_2& 3& 4& 35\end{array}$

Q.

The following table gives the marks obtained by the students of a class in an exam out of 50.

$\begin{array}{cc}\text{Marks}& \text{No. of Students}\\ Below10& 5\\ Below20& 10\\ Below30& 23\\ Below40& 31\\ Below50& 40\end{array}$

(i) Convert the cumulative frequency distribution into a regular frequency distribution.

(ii) Find the mean. [3 MARKS]

Q. Consider the frequency distribution of the given number
$\begin{array}{ccccc}Value:& 1& 2& 3& 4\\ Frequency:& 5& 4& 6& f\end{array}$
​If the mean is known to be 3, then the value of $f$ is ____.

1. 10
2. 15
3. 14
4. 3

Q. If the values $1,\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{5},....\frac{1}{n}$ occur at frequencies $1,2,3,4,5,\mathrm{6...},n$ respectively, in a frequency distribution, then the mean is

1. $1$
2. $\frac{1}{n}$
3. $n$
4. $\frac{2}{n+1}$

Q.

Find the vale of p for the following frequency distribution whose mean is 16.6
$\begin{array}{cccccccc}\text{x}& 8& 12& 15& p& 20& 25& 30\\ \text{f}& 12& 16& 20& 24& 16& 8& 4\end{array}$

Q. Standard deviation about mean $\left(\overline{x}\right)$ for a given discrete frequency distribution $x_1,x_2,x_3,.....x_n$ with frequencies $f_1,f_2,f_3,...f_n$ is :

1. $\sqrt{{\sum }_{i=1}^n\frac{(x_i-\overline{x}{)}^2}{n}}$
2. $\sqrt{\frac{{\sum }_{i=1}^{n}fi(x_i-\overline{x}{)}^2}{{\sum }_{i=1}^{n}fi}}$
3. $\frac{\sqrt{{\sum }_{i=1}^{n}fi(x_i-\overline{x}{)}^2}}{{\sum }_{i=1}^{n}fi}$
4. $\sqrt{\frac{{\sum }_{i=1}^{n}fi(x_i-\overline{x}{)}^2}{n}}$

Q.

Find the vale of p for the following frequency distribution whose mean is 16.6
$\begin{array}{cccccccc}\text{x}& 8& 12& 15& p& 20& 25& 30\\ \text{f}& 12& 16& 20& 24& 16& 8& 4\end{array}$

Q.

Find the vale of p for the following frequency distribution whose mean is 16.6
$\begin{array}{cccccccc}\text{x}& 8& 12& 15& p& 20& 25& 30\\ \text{f}& 12& 16& 20& 24& 16& 8& 4\end{array}$

Q.

Find the mean age in years from the frequency distribution given below:
$\begin{array}{cc}Classintervalofageinyears& Frequency\left(f_i\right)\\ 25-29& 4\\ 30-35& 14\\ 35-39& 22\\ 40-45& 16\\ 45-49& 6\\ 50-55& 5\\ 55-59& 3\\ Total& 70\end{array}$

1. 39.35

2. 29.39

3. 40.15

4. 40.39