Measures of Dispersion
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Box 3: Food vs. Oil
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Below are the figures for foodgrain procurement and crude oil production during 20x1-x2
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Month
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Foodgrain Procurement
('000 tonnes)
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Crude Oil Production
(lakh tonnes)
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20x1
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April
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3,506
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23.5
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May
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3,558
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23.2
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June
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285
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22.3
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July
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65
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23.0
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August
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25
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22.9
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September
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782
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22.1
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October
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2,473
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22.6
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November
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1,920
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21.8
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December
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2,403
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22.6
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20x2
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January
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2,300
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22.6
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February
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1,603
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20.1
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March
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837
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22.4
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Total
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19,757
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269.1
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The variability of the crude oil figures is much less than those of the foodgrain figures. This can be seen from the fact that all the crude oil production figures lie within 11% of the mean value of 22.4 lakh tonnes (i.e. between 19.9 lakh tonnes and 24.9 lakh tonnes). On the other hand only one foodgrain figure, i.e. February 20x2 procurement lies within 11% of the mean procurement value of 1646.4 thousand tonnes (between 1465.3 lakh tonnes and 1827.5 lakh tonnes). Hence the mean is a more representative value for the crude oil data as compared with the foodgrain data.
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In the case of foodgrain procurement, the monthly figures vary from a low of 25 thousand tonnes in August 20x1 to a high of 3558 thousand tonnes in May 20x1. This is due to the seasonal nature of agriculture.
In the case of crude oil production, the monthly figures vary from a low of 20.1 lakh tonnes in February 20x2 to a high of 23.5 lakh tonnes in April 20x1.
The above vignette reveals that while a mean may give the central tendency of data, it does not reveal anything about the variability or dispersion of the data. For this another measure is needed.
The variability or dispersion of data is given by measures of dispersion.
When there is no dispersion, all the data points have identical values and the values of all the measures of central tendency converge.