Dispersion,measure of disperion, absolute and relative dispersion

New Presentation of Statistics

1. Statistics Name : ABC Roll no : Nothing Teacher : ABC

2. Dispersion The scatterness of given values about their center is called dispersion.

3. Measure of dispersion Any descriptive measure that indicates the amount of variation of given values about their center is called measure of dispersion. It is divided in to two types : Absolute dispersion. Relative dispersion.

4. Absolute Relative dispersion dispersion Any descriptive measure that indicates the amount of variation of given values about their center in the same unit or in the square of given unit is called absolute measure of dispersion. Any unit free measure that indicates the amount of variation of given values about their center is called relative measure of dispersion.

5. Sub-types Sub-types of absolute dispersion: Range Quartile deviation Mean deviation Variation Sub-types of relative dispersion: Coefficient of range Coefficient of quartile Coefficient of mean deviation Coefficient of variation

6. Range Coefficient of range The difference between largest (L) and smallest (S) value of given data set is called its range. ( X ‹m › - X‹n › ) If X has values X 1 , X2 up to Xn with largest values Xm and smallest values X1 than coefficient of range can be define as:

7. Quartile deviation It is half of the difference between upper and lower quartiles of given data If a variable X has X1 , X2 up to Xn values with upper quartile Q3 and lower quartile Q1than its coefficient of quartile deviation can be defined as

8. Mean deviation The mean of absolute deviation of given values from their mean , median or mode is called mean deviation. If a variable X has N values X1 , X2 up to Xn with mean deviation and average m than its coefficient of mean deviation can be defined as:

9. Variance The mean of squared deviations of given values from their mean is called variance. If a variable X has N values X1 , X2 up to Xn values with standard deviation (S) and mean X- its coefficient of variation can be defined as: