MEASURES OF DISPERSION

1. Measures of Dispersion
Submitted to :
Dr. Priyanka Shankar
Assistant Professor
BBAU, Lucknow
Submitted by :
Alka Nanda
Ph.D. Scholar (1st Semester)
Enrolment No. – 1720/20

2.  Dispersion means scatter, deviation, spread or fluctuation.
 It denotes the lack of uniformity in item values of a given data.
 Value away from the central value or average, is called Dispersion.
 Greater the variation amongst different items of a series, the more
will be the dispersion.
 As per Bowley, “Dispersion is a measure of the variation of the
items”.
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DISPERSION

3. To determine the reliability of an average
To compare the variability of two or more series
For facilitating the use of other statistical measures
Basis of Statistical Quality Control
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OBJECTIVES OF MEASURING DISPERSION

4.  Easy to understand
 Simple to calculate
 Uniquely defined
 Based on all observations
 Not affected by extreme observations
 Capable of further algebric treatment
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PROPERTIES OF A GOOD MEASURE OF
DISPERSION

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METHODS OF MEASURING DISPERSION
RANGE
SEMI-INTER QUARTILE RANGE OR QUARTILE
DEVIATION
MEAN DEVIATION OR AVERAGE DEVIATION
STANDARD DEVIATION
VARIANCE

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RANGE (R)
 Simplest measures of dispersion.
 It is defined as the difference between the largest and smallest values
in the series.
𝑹 = 𝑳 − 𝑺
R = Range
L = Largest Value,
S = Smallest Value
 Coefficient of Range =
𝑳 −𝑺
𝑳+𝑺

7. RANGE
 Simple to understand
 Easy to calculate
 Widely used in statistical quality
control
MERITS
 Can’t be calculated in open ended
distributions
 Not based on all the observations
 Affected by sampling fluctuations
 Affected by extreme values
DEMERITS
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8. QUARTILE DEVIATION (Q)
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o Quartile Deviation is half distance between 75th percentile i.e., 3rd quartile (Qɜ)
and 25th percentile, i.e., first quartile (Q1).
o In normal distribution quartile deviation is called Probable Error (PE).
Q1 = First quartile
Q2 = Median
Q3 = Third quartile

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QUARTILE DEVIATION (Q)

10. MEAN DEVIATION (M.D.)
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o Mean deviation of a series is arithmetic average of the
deviations of various items from a measure of central
tendency (Mean, Median, Mode).
o It is also called as Average Deviation.
For grouped data :
 Mean Deviation from Mean ( δ ) =
 Mean Deviation from Median ( δm ) =
 Mean Deviation from Mode ( δ ) =
Σ | X − Z |
𝑵
Where,
X = I value of variable x
N = Number of items
X
̄ = Arithmetic mean
M = Median
Z = Mode

11. MEAN DEVIATION
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12. STANDARD DEVIATION (σ)
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 Most important & widely used measure of dispersion.
 First used by Karl Pearson in 1893.
 Also called Root Mean Square deviations.
 It is defined as the square root of the arithmetic mean of the squares of the
deviation of the values taken from the mean.
 Denoted by σ (sigma).

13. CALCULATION
OF
STANDARD
DEVIATION
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INDIVIDUAL SERIES – ACTUAL MEAN METHOD
INDIVIDUAL SERIES – ASSUMED MEAN/ SHORTCUT METHOD
INDIVIDUAL SERIES – METHOD BASED ON USE OF ACTUAL DATA

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DISCRETE SERIES – ACTUAL MEAN METHOD
DISCRETE SERIES – ASSUMED MEAN/ SHORTCUT METHOD
DISCRETE SERIES – STEP DEVIATION METHOD
CONTINUOUS SERIES – STEP DEVIATION METHOD

16. VARIANCE (σ)
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 It is another measure of dispersion.
 It is the square of the Standard Deviation.
 Variance = (SD)² = σ²
COMBINED STANDARD DEVIATION

17. COEFFICIENT OF VARIATION (C.V.)
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 It was developed by Karl Pearson.
 It is an important relative measure of dispersion.
 It is used in comparing the variability, homogeneity, stability, uniformity &
consistency of two or more series.
 Higher the CV, lesser the consistency.

18. Thank you!
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