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Session 8 MEASURES Of DISPERSION
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Learning Objectives Why do we study dispersion? Measures of Dispersion Range Standard Deviation Variance
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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.
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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!
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Measures of Dispersion Measures of Dispersion Absolute Measures Relative Measures
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Measures of Dispersion Range Inter Quartile Range Quartile Deviation Variance Standard Deviation Mean Deviation
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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)
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MERITS OF RANGE Simple to understand easy to calculate Quickest way to get a measure of dispersion
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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
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USES OF RANGE Used for making quality control chart For study the fluctuation in financial and share market
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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
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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
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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.
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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.
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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.
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(a) Positive skewed, (b) Negative skewed
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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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