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Unit 6: Dispersion: Meaning and Characteristics, Absolute and Relative Measures of Dispersion including Range...

• Quartile is the location-based measure of dispersion. It measures the average amount by which Notes
the first and the third quartiles deviate from the second quartile i.e., median.
• In statistics, a percentile (or centile) is the value of a variable below which a certain percent of
observations fall. For example, the 20 percentile is the value (or score) below which 20 percent
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of the observations may be found. The term percentile and the related term percentile rank are
often used in the reporting of scores from norm-referenced tests. For example, if a score is in the
86 percentile, it is higher than 85% of the other scores.
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• In addition to the percentile function, there is also a weighted percentile, where the percentage in
the total weight is counted instead of the total number. There is no standard function for a
weighted percentile. One method extends the above approach in a natural way.
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• When ISPs bill “burstable” internet bandwidth, the 95 or 98 percentile usually cuts off the
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top 5% or 2% of bandwidth peaks in each month, and then bills at the nearest rate. In this way
infrequent peaks are ignored, and the customer is charged in a fairer way. The reason this
statistic is so useful in measuring data through put is that it gives a very accurate picture of the
cost of the bandwidth. The 95 percentile says that 95% of the time, the usage is below this
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amount. Just the same, the remaining 5% of the time, the usage is above that amount.
• In general terms, for very large populations percentiles may often be represented by reference
to a normal curve plot. The normal curve is plotted along an axis scaled to standard deviation,
or sigma, units. Mathematically, the normal curve extends to negative infinity on the left and
positive infinity on the right. Note, however, that a very small portion of individuals in a
population will fall outside the – 3 to + 3 range.
• Percentiles represent the area under the normal curve, increasing from left to right. Each standard
deviation represents a fixed percentile. Thus, rounding to two decimal places, – 3 is the 0.13 th
percentile, – 2 the 2.28 percentile, – 1 the 15.87 percentile, 0 the 50 percentile (both the mean
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and median of the distribution), + 1 the 84.13 percentile, + 2 the 97.72 percentile, and + 3 the
nd
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99.87 percentile. Note that the 0 percentile falls at negative infinity and the 100 percentile at
positive infinity.
6.5 Key-Words
1. Absolute measures : Absolute measures of Dispersion are expressed in same units in which
original data is presented but these measures cannot be used to compare
the variations between the two series. Relative measures are not expressed
in units but it is a pure number. It is the ratios of absolute dispersion to an
appropriate average such as co-efficient of Standard Deviation or Co-
efficient of Mean Deviation.
Relative measures : These measures are calculated for the comparison of dispersion in two or
more than two sets of observations. These measures are free of the units
in which the original data is measured. If the original data is in dollar or
kilometers, we do not use these units with relative measure of dispersion.
These measures are a sort of ratio and are called coefficients. Each absolute
measure of dispersion can be converted into its relative measure.
2. Quartile deviation : The quartile deviation is a slightly better measure of absolute dispersion
than the range. But it ignores the observation on the tails. If we take
difference samples from a population and calculate their quartile
deviations, their values are quite likely to be sufficiently different. This is
called sampling fluctuation. It is not a popular measure of dispersion.
The quartile deviation calculated from the sample data does not help us
to draw any conclusion (inference) about the quartile deviation in the
population.

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