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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

Typology: Study notes

2021/2022

Available from 11/06/2022

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Measures of Dispersion
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Download Measures of Dispersion: Basics to Advance and more Study notes Statistics in PDF only on Docsity!

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.