Saturday, January 30, 2010

Measure of Dispersion

Dispersion: - Dispersion refers to the scatteredness of the individual items of statistical series from their central value. So a descriptive measure of scatter of the values about the average is called measure of Dispersion.

The followings are the important methods for measure of dispersion:

  1. The Range
  2. The average/mean Deviation
  3. Quartile Deviation
  4. The 10 – 90 Percentile Range
  5. The Standard Deviation
  6. The Variance

The Range: - The Range of a set of numbers is the difference between the largest and smallest numbers in the set.

The average/mean Deviation: - The average/mean Deviation, of a set of N numbers X1, X2,……..XN is abbreviated MD and is defined by

Quartile Deviation: - Quartile Deviation, of a set of data is denoted by Q and defined by,Q = (Q 3 – Q1)/2

The 10 – 90 Percentile Range: - The 10 – 90 Percentile Range, of a set of data is defined by, 10 – 90 Percentile Range = P90 – P10

The Standard Deviation: - The Standard Deviation of a set of N numbers X1, X2,……..XN is denoted by σ and is defined by

The Variance: - The Variance of a set of data is defined as the square of the standard deviation and is thus given by σ2 and is denoted by

Co-efficient of Variation: - If the average of a statistical data is the mean x and if the absolute dispersion is the standard deviation, then the relative dispersion is called Co-efficient of dispersion. It is denoted by v and is given by, v = (σ/x) × 100

Problem: -

Find the standard deviation and co-efficient of variation of the class test of 100 students of XYZ University.

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