SS1 Third Term Further Mathematics Lesson Note – Measures of Dispersion

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WEEK 4

TOPIC: MEASURES OF DISPERSION

CONTENT:

• Range
• Inter-quartiles
• Mean deviation
• Standard deviation
• Variance
• Coefficient of variation

Range

Measures of Dispersion

The measure of dispersion (also called measure of variation) is concerned with the degree of spread of the numerical value of a distribution.

The Range:  This is the difference between the maximum and minimum values in the data.

Examples 1:

Find the range of the data 6, 6, 7, 9, 11, 13, 16, 21 and 32

Solution: The maximum item is 32

The minimum item is 6

∴ Range = 32 – 6 = 26

Examples 2:

The following shows the distribution of mails obtained by 20 students in a test:

58     55      52      56      64     71    64     53     54     67

66     68      78      52      65     57    61     65     59     52

Find the range.

Solution

The largest value in the distribution    =    78

The smallest value in the distribution =   52

Range    =    78 – 52 = 26

Inter-quartiles

The difference between the values of the third and first quartiles is called the inter-quartile range. In equation form, we state this as:

Inter-quartile range = Q₃ – Q₁

Inter-quartile range is a measure of spread.

Quartile deviation

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