Class 11 statistics Chapter 6 Measures of dispersion
NCERT Notes for Class 11 statistics Chapter 6 Measures of dispersion, (Statistics) exam are Students are taught thru NCERT books in some of state board and CBSE Schools. As the chapter involves an end, there is an exercise provided to assist students prepare for evaluation. Students need to clear up those exercises very well because the questions with inside the very last asked from those.
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NCERT Notes for Class 11 statistics Chapter 6 Measures of dispersion
Class 11 statistics Chapter 6 Measures of dispersion
Dispersion: The word Dispersion means deviation or difference. In statistics, dispersion refers to deviation of various items of the series from its Central value. It is also called averages of second order. Dispersion is two types. They are the following.
 Absolute Measures of Dispersion: It is expressed in the same statistical unit in which the original data are given.
 Relative Measures of Dispersion: It is the ratio of absolute dispersion to an appropriate average. It is independent of the unit .
Measures of Dispersion: The following are the important measures of Dispersion.
 Range ^{[1]}
 Quartile deviation
 Mean deviation
 Standard deviation
 Lorenz curve
Range:It is defined as the difference between the largest and the smallest value of the series.
Range=LS
Here L= largest value, S=smallest value
coefficient of Range = 𝐿−𝑆 / 𝐿+𝑆

Merits and Demerits of Range Merits:
 Easy to calculate
 Easy to understand Demerits:
 It is affected by extreme values
 It is not based on all observations
 It cannot be used in case of openend distribution.
Quartile Deviation: It is the average of the difference between the upper quartile (Q3) and the lower quartile (Q1).
Merits of quartile deviation
 Easy to calculate
 Easy to understand
 Not affected by extreme values
 More reliable than range
Demerits of quartile deviation
 It is not based on all observations
 It ignores the first 25% observations as well as the last 25%
 Not capable of further algebraic treatment
 It doesn’t measure variation of items^{2} from the average.
MEAN DEVIATION: Mean deviation of a series is the arithmetic average of the deviations of various items from a measure of Central tendency.
MERITS OF MEAN DEVIATION:
 Easy to calculate
 Easy to understand
 Rigidly defined
 Based on all items
 Not very much affected by extreme values
DEMERITS OF MEAN DEVIATION:
 Very much affected by sampling fluctuations
 Not capable of further algebraic treatment
 Ignoring signs reduces its application in scientific problems.
STANDARD DEVIATION: It is defined as the square root of the arithmetic average of the squares of deviations taken from the arithmetic average of a series.
SD in individual series =
SD in discrete and continuous series =
CO efficient of variation=
MERITS AND LIMITATIONS OF STANDARD DEVIATION
 It is the best measure of Dispersion
 It is capable of further algebraic treatment
 It is less affected by sampling fluctuations
 It is based on every item of the distribution
 The value is always definite
LIMITATIONS
 It is difficult to compute
 It gives more importance to extreme items
 It can not be used for purposes of comparison
INTERPRETATIONS
 If the value of Coefficient of Variation is less, it means it is more consistent.
 A series with more Coefficient of Variation is regarded as less consistent or less stable than a series with less coefficient of variation.
LORENZ CURVE
It is the graphical representation of Dispersion Developed by Dr. Max O. Lorenz
LORENZ CURVE STEPS
 Find Class Mid Point
 Cumulate the Class Mid Points
 Cumulate the frequencies ^{3}
 Take the grand total of class mid points and grand total of frequencies as 100
 Then convert all the other cumulative class mid points and cumulative frequencies into their respective percentages
 Mark cumulative percentages of frequencies on the x axis and cumulative class mid points on the y axis 7) Each axis should have values from 0 – 100.
 Draw a line from the origin to the point whose cordinate is 100, 100.
 This Line is called the LINE OF EQUAL DISTRIBUTION
 Then plot the cumulative values and cumulative frequencies.
MERITS AND LIMITATIONS MERITS
 It is most commonly used to show the various kinds of inequality.
 The curve uses the information expressed in a cumulative manner to indicate the degree of variability.
 It is especially useful in comparing the variability of two or more distributions.
 Since it gives a picture, it is easy to understand.
LIMITATIONS
 It does not give any numerical value of the measure of dispersion
 It merely gives a picture of the extent^{4} to which a series is pulled away from an equal distribution
Join those points to get a curve which is called LORENZ CURVE
INTERPRETATION (with reference to the given diagram)
Any curve similar to ‘OAC’ closer to the line of Equality ‘OC’ indicates high degree of equality or limited degree of inequality. The farther the curve OC, the greater is the variability present in the distribution. The farthest curve from the line ‘OC’ has the highest Dispersion