Dispersion is the measure of the variation of the items Some important definitions are given below Dispersion is the measure of extent to which individual items vary The measure of the ID: 1022114
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1. Measures Of Dispersion Dispersion is the measure of the variation of the items.Some important definitions are given below:“Dispersion is the measure of extent to which individual items vary.” “The measure of the scatteredness of the mass of figures in a series about an average is called the measure of variation or dispersion.”
2. Two types of measures of dispersion (i) Absolute measures of dispersion (ii) Relative measures of dispersion
3. Important Measures of Dispersion Following are some important measures of dispersion1. Range2. Interquartile Range and Quartile Deviation 3. Mean Deviation or Average Deviation4. Standard Deviation
4. RangeRange is the simplest measure of dispersion. Range (R) = Largest observation Smallest observation L = Largest observation S = Smallest observation R = Range Coefficient of Range =
5. QuartileQuartiles are those values of the variable, which divides the total frequency into four equal parts.Coefficient of Quartile: Coefficient of Quartile =
6. In case of Individual and discrete SeriesQ1 = Size of item of the seriesQ3 = Size of item of the series.
7. Average Deviation or Mean DeviationIt is the arithmetic average of the group measured from the average (Mean or Median or Mode taking all deviations as positive).
8. The Mean Deviation about mean or median or mode can be expressed as follows (i) Mean Deviation from Mean ( ) (ii) Mean Deviation from Median ( ) (iii) Mean Deviation from Mode ( )
9. Q. Find mean deviation about mean from the following data:3, 5, 6, 7, 8, 10, 11, 14Solution: Arithmetic Mean Mean Deviation From Mean
10. Standard Deviation (Root mean square deviation) The root-mean square deviation, denoted by s, is defined as the positive square root of the mean of the squares of the deviations from an origin A.A = Assumed Mean
11. Q. Calculate standard deviation(S.D.) from the following data:10, 11, 17, 25, 7, 13, 21, 10, 12, 14Solution.
12. Q. Find standard deviation (S. D.) from the following data:Size 4 5 6 7 8 9 10Frequency 6 12 15 28 20 14 5