Measures of Dispersion
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Measures of Dispersion: Basics to Advance, Study notes of Statistics
*Why Study Dispersion? *What is Dispersion? *Significance of Measuring Dispersion *Properties of Good Measure of Dispersion *The Range
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2021/2022
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Quantitative Aptitude & Business Statistics:
Measures of Dispersion
Why Study 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
Coefficient of Range iscalculated as,
Coefficient of Range =
S
L
S
L
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
S
L
S
L
Quantitative Aptitude & Business Statistics:
Measures of Dispersion
Limitations of Range
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
Limitations of Range
It does not indicate thedirection of variability.
It does not present veryaccurate picture of thevariability.