Chapter – 11 Measures of Dispersion: Chapter – 11 Measures of Dispersion
What is Dispersion????: What is Dispersion???? The degree to which numerical data tend to spread about an average value is called the variation or dispersion of the data.
Absolute and Relative measures of dispersion: Absolute and Relative measures of dispersion
Some Formulas: Some Formulas Range R = Upper Limit of the Last Class Interval – Lower Limit of the First Class Interval Or R = H – L Where R=Range; H=Highest value in the series; L=Lowest value in the series Coefficient of range CR = H – L H + L Where CR=Coefficient of range; H=Highest value in the series; L=Lowest value in the series
Inter quartile range and quartile deviation and their coefficient: Inter quartile range and quartile deviation and their coefficient Inter Quartile Range = Q3 – Q1 Quartile Deviation = Q3 – Q1 2 Also called Semi-inter Quartile Range Coefficient of Quartile Deviation Coefficient of QD= Q3 – Q1 ÷ Q3 + Q1 = Q3 – Q1 2 2 Q3 + Q1
Quartile Deviation: Quartile Deviation
Mean Deviation: Mean Deviation Mean deviation is the arithmetic average of deviations of all the values consideration taken from a statistical average (mean, median or mode) of series. In taking deviation of values, algebraic signs + and – are not taken into consideration, that is negative deviations are also treated as positive deviations
Some other FORMULAs: Some other FORMULAs If deviations are taken from median MD m = ∑ | X – M | or ∑ | dm | N N If deviations are taken from arithmetic average MD x = ∑ | X – X | or ∑ | d x | N N Where, MD = Mean deviation ; X – M = Deviation from the median ; X - X = deviation from the arithmetic average ; N = Number of items
Coefficient of mean deviation: Coefficient of mean deviation Coefficient of MD from Mean = MD x X = Mean Deviation Arithmetic Mean Coefficient of MD from Median = MD m M = Mean Deviation Median Coefficient of MD from Mode = MD z Z = Mean Deviation Mode
MEan Deviation: MEan Deviation
stANDARD DEVIATION: stANDARD DEVIATION Standard Deviation is the Square root of the Arithmetic Mean of the squares of deviations of the items from their mean value. This is generally denoted by (sigma) of the Greek language. COEFFICIENT OF STANDARD DEVIATION = σ X
Standard Deviation: Standard Deviation
Lorenz Curve: Lorenz Curve Lorenz Curve is a measure of deviation of actual distribution from the line of equal distribution. Lorenz curve as a measure of dispersion is presently applied to the following parameters, viz., Distribution of income Distribution of wealth Distribution of wages Distribution of profits Distribution of production Distribution of population