Session 8MEASURES Of DISPERSION

Learning Objectives Why do we study dispersion? Measures of Dispersion

Range Standard Deviation Variance

DISPERSION

Definition : Dispersion is the degree of the

scatter of observation about a central values.

It is the degree of variation of the variable about central tendency.

CENTRAL TENDENCY Means:

Family A: (0+4+8+12+16+20)/6 = 60/6 = 10

Family B: (4+8+8+12+12+16)/6 = 60/6 = 10

Family C: (0+0+0+20+20+20)/6 = 60/6 = 10

Medians: For each, average the middle two & get 10

But the distributions clearly differ!

Measures of DispersionMeasures ofDispersion

Absolute Measures

Relative Measures

Measures of Dispersion

Range

Inter Quartile Range

Quartile Deviation Variance

Standard Deviation

Mean Deviation

RANGE It is the difference between the value

of smallest observation and the value of the largest observation present in the distribution.

R = L-S

Coefficient of Range= (L-S)/(L+S)

MERITS OF RANGE Simple to understand easy to calculate Quickest way to get a measure of

dispersion

LIMITATIONS OF RANGE

Not based on all observation Influenced by extreme value It Cannot computed for open – end

data It Fail to explain the scatter around

average

USES OF RANGE

Used for making quality control chart For study the fluctuation in financial

and share market

Variance

Definition Variance is average squared deviation from arithmetic mean Ungrouped data σ²=Σ(x-x)² n Grouped data σ²=Σf(x-x)² n

Standard Deviation Standard Deviation is the square root of the varianceStandard deviation is also known as root of mean squared deviation. For ungrouped data S.D. (σ)= Σ(x-x )² n For Grouped data S.D.(σ )= Σ(x-x )² n

Properties of Standard Deviation Standard Deviation is independent of

change of origin. Standard Deviation is dependent on

the change of scale. Standard Deviation is the minimum

root-mean squared deviation.

Coefficient of variation Coefficient of variation is relative measure

of dispersion based on S.D.

Coefficient of Variation= S.D./Mean

Coefficient of variation is used in problem situation where we want to compare the variability, homogeneity, stability, uniformity & consistency of two or more data set.

Skewness and Kurtosis

Skewness is refer to the study of the frequency distribution curve.

Kurtosis is concerned with the flatness or peakness of the frequency distribution curve.

(a) Positive skewed, (b) Negative skewed

Difference between Dispersion & Skewness

Dispersion is concern with the amount of variation rather than with its direction.

Skewness tell us about the direction of the variation.