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Session 8 MEASURES Of DISPERSION. Learning Objectives  Why do we study dispersion?  Measures of Dispersion Range Standard Deviation Variance.

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Presentation on theme: "Session 8 MEASURES Of DISPERSION. Learning Objectives  Why do we study dispersion?  Measures of Dispersion Range Standard Deviation Variance."— Presentation transcript:

1 Session 8 MEASURES Of DISPERSION

2 Learning Objectives  Why do we study dispersion?  Measures of Dispersion Range Standard Deviation Variance

3 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.

4 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!

5 Measures of Dispersion Measures of Dispersion Absolute Measures Relative Measures

6 Measures of Dispersion Range Inter Quartile Range Quartile Deviation Variance Standard Deviation Mean Deviation

7 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)

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

9 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

10 USES OF RANGE  Used for making quality control chart  For study the fluctuation in financial and share market

11 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

12 Standard Deviation Standard Deviation is the square root of the variance Standard 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

13 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.

14 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.

15 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.

16 (a) Positive skewed, (b) Negative skewed

17 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.


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