Measure of dispersion and it’s need Presented and made by waseem javid

1. Measure of dispersion and it’s
need
Presented by waseem javid
Course:- BSc radiology(5thsem)
Subject:- Research methodology &
Biostatistics

2. Definition
Measure of dispersion are descriptive statistics that
describe how similar a set of scores are to each other.
1. The more similar the scores are to each other, the
lower the measure of dispersion will be.
2. The less similar the scores are each other, the
higher the measure of dispersion will be.
3. In general, the more spread out a distribution is ,
the larger the measure of dispersion will be.

3. Objectives of measure of dispersion
To determine the reliability of an average.
To compare the variability of two or more series.
For facilitating the use other statistical measures.

4. Methods of measuring dispersion
Range
Interquartile range and quartile
deviation
Mean deviation
Standard deviation
Coefficient of variation
Lorenz curve

5. Range
It is the simplest measure of dispersion .
It is defined as the difference between the largest
and smallest values in the series.
R=L –S
R = range , L= largest Value, S= smallest value.
Coefficient of range = L-S</L+S

6. Interquartile range and quartile
Deviation
Inquartile range is the difference between the upper
quartile(Q3) and lower quartile (Q1).
It covers dispersion of middle 50% of the items of the
series .
Symbolically ,Inquartile range =Q3-Q1

7. Mean deviation
It is also called Average Deviation.
It is defined as the arithmetic average of the
deviation of the various items of a series computed
from measures of central tendency like mean or
median.

8. Standard deviation
Most important and widely used measure of
dispersion and is also called root mean square
deviations.
First used by Karl Pearson in 1893 .
It is defined as the square root of the arithmetic
mean of the squares of the deviation of the values
taken from the mean.
Denoted by sigma.

9. Coefficient of variance (CV)
It was developed by karl Pearson .
It is an important relative measure of dispersion.
It is used in comparing the variability, homogeneity,
stability, uniformity and consistency of two or more
series .
Higher the CV, lesser the consistency.

10. Lorenz curve
It is a graphical method of studying dispersion .
It was given by famous statistician MAX O LORENZ.
It has great utility in the study of degree of inequality
in distribution of income and wealth