Notes On Introduction to Dispersion - CBSE Class 11 Maths

Statistics is a branch of mathematics that deals with the collection, classification and analysis of numerical data.

The table shows the data of marks scored by a student in eight subjects.

         Rohan    52    55    57    59    61    63    65    68

Representation of this data as dots on the number line:

The data is scattered along the line.

Statistics that signify the extent of the spread of items around the measure of the central tendency is known as dispersion. It is a single number to describe the variability.

To decide the performance, the variability of the extent of the numerical values is necessary, which is called the central dispersion.

Methods to find central dispersion:

  • Range
  • Quartile deviation
  • Mean deviation
  • Standard deviation

Range

The range of a distribution is the difference between the greatest and the least values observed.

Range = Maximum value - Minimum value

Ex: Consider the data of marks scored by Rohan and Dinesh in eight subjects.

       Rohan    52    55    57    59    61    63    65     68
       Dinesh    29    38    42    58    62    74    83     94

Range of the marks scored by Rohan = 68 - 52 = 16

Range of the marks scored by Dinesh = 94 - 29 = 65

The important measures of dispersion, which depend upon the deviations of the observations from a central tendency, are mean deviation and standard deviation.

Summary

Statistics is a branch of mathematics that deals with the collection, classification and analysis of numerical data.

The table shows the data of marks scored by a student in eight subjects.

         Rohan    52    55    57    59    61    63    65    68

Representation of this data as dots on the number line:

The data is scattered along the line.

Statistics that signify the extent of the spread of items around the measure of the central tendency is known as dispersion. It is a single number to describe the variability.

To decide the performance, the variability of the extent of the numerical values is necessary, which is called the central dispersion.

Methods to find central dispersion:

  • Range
  • Quartile deviation
  • Mean deviation
  • Standard deviation

Range

The range of a distribution is the difference between the greatest and the least values observed.

Range = Maximum value - Minimum value

Ex: Consider the data of marks scored by Rohan and Dinesh in eight subjects.

       Rohan    52    55    57    59    61    63    65     68
       Dinesh    29    38    42    58    62    74    83     94

Range of the marks scored by Rohan = 68 - 52 = 16

Range of the marks scored by Dinesh = 94 - 29 = 65

The important measures of dispersion, which depend upon the deviations of the observations from a central tendency, are mean deviation and standard deviation.

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