Study MaterialsCBSE NotesStatistics Class 11 Notes Maths Chapter 15

Statistics Class 11 Notes Maths Chapter 15

CBSE Class 11 Maths Notes Chapter 15 Statistics

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.

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    Mean Deviation
    Mean deviation for ungrouped data
    For n observations x1, x2, x3,…, xn, the mean deviation about their mean \(\bar { x }\) is given by
    Statistics Class 11 Notes Maths Chapter 15 1

    Mean deviation about their median M is given by
    Statistics Class 11 Notes Maths Chapter 15 2

    Mean deviation for discrete frequency distribution
    Let the given data consist of discrete observations x1, x2, x3,……., xn occurring with frequencies f1, f2, f3,……., fn respectively in case
    Statistics Class 11 Notes Maths Chapter 15 3

    Mean deviation about their Median M is given by
    Statistics Class 11 Notes Maths Chapter 15 4

    Mean deviation for continuous frequency distribution
    Statistics Class 11 Notes Maths Chapter 15 5
    where xi 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, ……xn be n observations with \(\bar { x }\) as the mean, then the variance denoted by σ2, is given by
    Statistics Class 11 Notes Maths Chapter 15 6

    Standard deviation
    If σ2 is the variance, then σ is called the standard deviation is given by
    Statistics Class 11 Notes Maths Chapter 15 7

    Standard deviation of a discrete frequency distribution is given by
    Statistics Class 11 Notes Maths Chapter 15 8

    Standard deviation of a continuous frequency distribution is given by
    Statistics Class 11 Notes Maths Chapter 15 9

    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
    Statistics Class 11 Notes Maths Chapter 15 10

    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.

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