CBSE Class 11 Maths Chapter 15 Statistics Notes

Measure of Dispersion
The dispersion is the measure of variations in the values of the variable. It measures the degree of scatteredness of the observation in a distribution around the central value.

Range
The measure of dispersion which is easiest to understand and easiest to calculate is the range.
Range is defined as the difference between two extreme observation of the distribution.
Range of distribution = Largest observation – Smallest observation.

Mean Deviation
Mean deviation for ungrouped data
For n observations x₁, x₂, x₃,…, x_n, the mean deviation about their mean $\bar { x }$ is given by

Mean deviation about their median M is given by

Mean deviation for discrete frequency distribution
Let the given data consist of discrete observations x₁, x₂, x₃,……., x_n occurring with frequencies f₁, f₂, f₃,……., f_n respectively in case

Mean deviation about their Median M is given by

Mean deviation for continuous frequency distribution

where x_i are the mid-points of the classes, $\bar { x }$ and M are respectively, the mean and median of the distribution.

Variance
Variance is the arithmetic mean of the square of the deviation about mean $\bar { x }$ .
Let x₁, x₂, ……x_n be n observations with $\bar { x }$ as the mean, then the variance denoted by σ², is given by

Standard deviation
If σ² is the variance, then σ is called the standard deviation is given by

Standard deviation of a discrete frequency distribution is given by

Standard deviation of a continuous frequency distribution is given by

Coefficient of Variation
In order to compare two or more frequency distributions, we compare their coefficient of variations. The coefficient of variation is defined as

Note: The distribution having a greater coefficient of variation has more variability around the central value, then the distribution having a smaller value of the coefficient 0f variation.