Master the meaning of dispersion in CBSE Class 11 Applied Mathematics. Learn to measure data variability with clear examples, formulas, and exercises.
Dispersion refers to the extent to which values in a data set are spread around a central tendency, such as the mean or median. While measures of central tendency provide a single representative value, dispersion quantifies the reliability and consistency of that average. For example, if two classes have the same mean score of 70, the class with lower dispersion has more students scoring near 70.
Step 1: Identify the data set: {12, 15, 22, 28, 35}.
Step 2: Find the maximum value (35) and minimum value (12).
Step 3: Apply the formula: Range = 35 − 12 = 23.
Answer: The range of the data set is 23.
Absolute measures of dispersion are expressed in the same units as the original data, such as kilograms or rupees, making them unsuitable for comparing different data sets. Relative measures, known as coefficients, are unit-free ratios that allow for the comparison of variability between two distinct data sets. A coefficient of dispersion is calculated by dividing the absolute measure by a central value.
Step 1: Given data: {10, 20, 30, 40, 50}.
Step 2: Max = 50, Min = 10.
Step 3: Coefficient = (50 − 10) / (50 + 10) = 40 / 60 = 0.67.
Answer: The coefficient of range is 0.67.
A good measure of dispersion should be rigidly defined, easy to calculate, and based on all observations in the data set. It should also be capable of further algebraic treatment and remain unaffected by sampling fluctuations. Dispersion is zero only when all observations in the data set are identical.
Step 1: Data set: {5, 5, 5}.
Step 2: Mean (μ) = (5+5+5)/3 = 5.
Step 3: Dispersion = Σ(5-5)²/3 = 0.
Answer: Since all values are identical, the dispersion is 0.