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1. Dispersion refers to the variation of the items around an average.
2. Objectives of Dispersion
a) To determine the reliability of an average.
b) To compare the variability of two or more series.
c) It serves the basis of other statistical measures such as correlation etc.
d) It serves the basis of statistical quality control.
a) It should be easy to understand.
b) Easy to calculate.
c) Rigidly defined
d) Based on all observations.
e) Should not be unduly affected by extreme values.
a) Range
b) Quartile Deviation
c) Mean Deviation
d) Standard Deviation
a) Coefficient of Range
b) Coefficient of Quartile Deviation
c) Coefficient of Mean Deviation
d) Coefficient of Variation
Range
It is the difference between the largest and smallest value of distribution.
Computation of Range
Range = L – S
1. It is simple to understand and easy to calculate.
2. It is widely used in statistical quality control.
1. It is affected by extreme values in the series.
2. It cannot be calculated in case of open end series.
3. It is not based on all items.
Inter quartile range is the difference between Upper Quartile (Q3) and Lower Quartile Q1.
Quartile deviation is half of inter quartile range.
Computation of Inter quartile range and quartile deviation
1. Easy to compute
2. Less affected by extreme values.
3. Can be computed in open ended series.
1. Not based on all observations
2. It is influenced by change in sample and suffers from instability.
Mean Deviation is defined as the arithmetic average of the absolute deviations [ignoring signs] of various items from Mean or Median.
1. Based on all observations.
2. It is less affected by extreme values.
3. Simple to understand and easy to calculate.
1. It ignores ± signs in deviations.
2. It is difficult to compute when deviations comes in fractions.
It is defined as the root mean square deviation.
1. Value of its deviation is taken from Arithmetic Mean.
2. + and – signs of deviations taken from mean are not ignored.
i. Rigidly defined
ii. Based on all observations
iii. Takes Algebraic signs in consideration
iv. Amenable to further Algebraic treatment
i. Difficult to understand and compute.
ii. Affected by extreme items.
It is a graphical method of studying dispersion.
Lorenz curve is a cumulative percentage curve in which the percentage of frequency is combined with percentage of other items such as profit, income etc.
1 mark questions
1. What is range?
2. What is coefficient of variation?
3. What is Lorenz curve?
3 marks question
1.Mention any two merit and demerits each of Mean Deviation.
4 marks questions
1. Find out range and coefficient of range of the following series.
2. Find out Standard deviation (6) from the following data:
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