Question

What is mean deviation continuous frequency distribution?

Answer 1

Mean deviation continuous frequency distribution.

There are two ways to arrange the data in groups :

• Discrete frequency distribution
• Continuous frequency distribution

Representation of data in a tabular or graphical form which indicates the frequency (number of times an observation occurs within a particular interval) is known as a frequency distribution.

In frequency distribution of continuous type, the class intervals or groups are arranged in such a way that there are no gaps between the classes and each class in the table has its respective frequency.

Items	$0-5$	$5-10$	$10-15$	$15-20$	$20-25$
Frequency	$2$	$5$	$1$	$3$	$1$

In case of continuous series, a mid point is computed as $\frac{\mathrm{lower}\mathrm{limit}+\mathrm{upper}\mathrm{limit}}{2}$ and

Mean Deviation is computed using following formula.

$MD=\frac{\sum f|x-Me|}{N}=\frac{\sum f|D|}{N}$

Where

$N$ is Number of observations.

$f$ is Different values of frequency f.

$x$ is Different values of mid points for ranges.

$Me$ is mean.

Now,

Class interval	$f_i$	$x_i$	$f_i$$x_i$	$\left|x_i-\overline{x}\right|$	$f_i$$\left|x_i-\overline{x}\right|$
$0-5$	$2$	$2.5$	$5$	$-6.7$	$-13.4$
$5-10$	$5$	$7.5$	$37.5$	$-1.7$	$-8.5$
$10-15$	$1$	$12.5$	$12.5$	$3.3$	$3.3$
$15-20$	$3$	$17.5$	$52.5$	$8.3$	$24.9$
$20-25$	$1$	$22.5$	$22.5$	$13.3$	$13.3$
	$N=\sum _{i=1}^5{f}_i=12$		$$\begin{gathered} \mathrm{Mean}\left(\overline{x}\right)=\frac{\sum _{i=1}^5{f}_i{x}_i}{\sum _{i=1}^5{f}_i} \\ =\frac{110}{12} \\ =9.16 \end{gathered}$$		$$\begin{gathered} MD=\frac{\sum _{i=1}^5{f}_i\left|x_i-\overline{x}\right|}{\sum _{i=1}^5{f}_i} \\ =\frac{19.6}{12} \\ =1.63 \end{gathered}$$