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*Why Study Dispersion? *What is Dispersion? *Significance of Measuring Dispersion *Properties of Good Measure of Dispersion *The Range
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Quantitative Aptitude & Business Statistics:
Measures of Dispersion
An average, such as the meanor the median only locates thecentre of the data.
An average does not tell usanything about the spread ofthe data.
Quantitative Aptitude & Business Statistics:
Measures of Dispersion
Significance of Measuring
Dispersion
To determine the reliability ofan average.
To facilitate comparison.
To facilitate control.
To facilitate the use of otherstatistical measures.
Quantitative Aptitude & Business Statistics:
Measures of Dispersion
Properties of Good Measure of
Dispersion
Simple to understand and easyto calculate
Rigidly defined
Based on all items
A meanable to algebraictreatment
Sampling stability
Not unduly affected by Extremeitems.
Quantitative Aptitude & Business Statistics:
Measures of Dispersion
Relative measures of Dispersion
Based on Selecteditems
Based onall items
1.Coefficient of
Range 2.Coefficient of QD
1.Coefficient of MD 2.Coefficient of SD & Coefficient of Variation
Quantitative Aptitude & Business Statistics:
Measures of Dispersion
A small value for a measure ofdispersion indicates that the dataare clustered closely (the mean istherefore representative of the data).
A large measure of dispersionindicates that the mean is notreliable (it is not representative ofthe data).
Quantitative Aptitude & Business Statistics:
Measures of Dispersion
RANGE = Highest Value -Lowest Value
Quantitative Aptitude & Business Statistics:
Measures of Dispersion
The range only takes intoaccount the most extremevalues.
This may not berepresentative of thepopulation.
Quantitative Aptitude & Business Statistics:
Measures of Dispersion
Coefficient of Range iscalculated as,
Coefficient of Range =
Quantitative Aptitude & Business Statistics:
Measures of Dispersion
From the following datacalculate Range andCoefficient of Range
Marks
5
15
25
35
45
55
No .ofStudents
10
20
30
50
40
30
Quantitative Aptitude & Business Statistics:
Measures of Dispersion
From the following data ,calculateRange and Coefficient of Range
Marks
0-
10-
20-
30-
40-
50-
No .ofStudents
10
20
30
50
40
30
Quantitative Aptitude & Business Statistics:
Measures of Dispersion
Lower limit of lowest class(S)=
Upper limit of highest class(L)=
Coefficient of Range
Quantitative Aptitude & Business Statistics:
Measures of Dispersion
It does not take intoaccount of all items ofdistribution.
Only two extreme values aretaken into consideration.
It is affected by extremevalues.
Quantitative Aptitude & Business Statistics:
Measures of Dispersion
It does not indicate thedirection of variability.
It does not present veryaccurate picture of thevariability.