The procedure for computing quartiles, deciles and percentiles are the same as the median.

Computations for Related positional measure

The procedure for computing quartiles, deciles and percentiles are the same as the median.

1. Arrange the data either in ascending or descending order of magnitude.

2. Apply the formula

Example 8.1

Find *D*2 and *D*6 for the following series 22, 4, 2, 12, 16, 6, 10, 18, 14, 20, 8

*Solution :*

Here *n* = 11 observations are arranged into ascending order 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22

*D*2* *= size of 2.4th value â‰ˆsize of 2nd value = 4

*D*6* *= size of 7.2th* *value â‰ˆsize of 7th* *value =14

Example 8.2

Calculate the value of Q1, Q3, D6 and P50 from the following data

Steps:

1. Arrange the data in ascending or descending order of magnitude.

2. Find out cumulative frequencies.

3. Apply the formula:

Now look at the cumulative frequency (*cf*) column and find that total which is either equal to ( N+1 / 4 ) or next higher than that and determine the value of the variable corresponding to this. That gives the value of *Q*1. Similarly *Q*3 is determined with reference of 3(N+1) / 4 value of the variable.

Example 8.3

Compute *Q*1, *D*2 and *P*90 from the following data

*Solution :*

In the case of continuous frequency distribution, the classes are arranged either in ascending or descending order and the class corresponding to the cumulative frequency (cf ) just equal or greater than (N/4) is called Q1 class and the value of Q1is obtained by the following formula:

where *L* is the lower limit of the *Q*1 class,

*f* is the frequency of the *Q*1 class,

*c *is the magnitude of the* Q*1* *class,

*pcf *is the cumulative frequency of the pre* Q*1* *class.

Similarly third quartile value can be obtained by the same procedure with Q3class by the following formula:

where *L* is the lower limit of the third quartile class,

*f *is the frequency of the third quartile class,

*c *is the magnitude of the third quartile class,

*pcf *is the cumulative frequency of the pre* Q*3* *class

Similarly the same procedure is to be followed for other positional measures such as deciles and percentiles,

Example 8.4

Compute upper Quartiles, lower Quartiles, D4 and P60, P75 from the following data

*Solution:*

Tags : Measures of central tendency , 11th Business Mathematics and Statistics(EMS) : Chapter 8 : Descriptive statistics and probability

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11th Business Mathematics and Statistics(EMS) : Chapter 8 : Descriptive statistics and probability : Computations for Related positional measure | Measures of central tendency

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