1. Quartiles, 2.Deciles 3. Percentiles

**Partition
Measures**

There
are three quartiles denoted by *Q*_{1}, *Q*_{2} and *Q*_{3} divides the frequency
distribution in to four equal parts

That is 25 percent of data will lie below *Q*_{1}, 50 percent of data below *Q*_{2} and 75 percent below *Q*_{3}. Here *Q*_{2}
is called the Median. Quartiles are obtained in almost the same way as median

If the data set consist of n items and arranged in ascending
order then

Compute *Q*_{1}
and *Q*_{3} for the data
relating to the marks of 8 students in an examination given below 25, 48, 32,
52, 21, 64, 29, 57

n = 8

Arrange the values in ascending
order

21, 25, 29, 32, 48, 52,
57, 64 we have

**Quartiles for Discrete Series
(grouped data)**

**Step 1: **Find cumulative
frequencies

**Step 2 **: Find ((N+1)/ 4)

**Step 3 **: See in the
cumulative frequencies, the value just greater than ((N+1)/ 4) the
corresponding value of *x* is *Q*_{1}

**Step 4 **: Find 3((N+1)/ 4)

**Step 5 **: See in the
cumulative frequencies, the value just greater than 3((N+1)/ 4) then the
corresponding value of *x* is *Q3*.

Compute *Q*_{1}
and *Q*_{3} for the data
relating to age in years of 543 members in a village

**Step 1: **Find cumulative
frequencies

**Step 2 **: Find (N/4)

**Step 3 **: *Q*_{1}* *class is
the class interval corresponding to the value of the cumulative frequency just
greater than (N/4)_{}

**Step 4 **: Q3 class is the
class interval corresponding to the value of the cumulative frequency just
greater than 3 (N/4)

Calculate the quartiles *Q*_{1}
and *Q*_{3} for wages of the
labours given below

Deciles are similar to quartiles. Quartiles divides ungrouped
data into four quarters and Deciles divide data into 10 equal parts .

Find the D_{6} for the following data

11, 25, 20, 15, 24, 28, 19, 21

Arrange in an ascending order

11,15,19,20,21,24,25,28

Calculate *D*_{5}
for the frequency distribution of monthly income of workers in a factory

The percentile values divide the frequency distribution into 100
parts each containing 1 percent of the cases. It is clear from the definition
of quartiles, deciles and percentiles

Relationship

P_{25} = Q_{1}

P_{50} = Median = Q_{2}

P_{75} = 3rd quartile = Q_{3}

The following is the monthly income (in 1000) of 8 persons
working in a factory. Find *P*_{30}
income value

10,14, 36, 25, 15, 21, 29, 17

Arrange the data in an ascending order.

n = 8

10,14,15,17,21,25,29,36

Calculate *P*_{61}
for the following data relating to the height of the plants in a garden

Tags : Formula, Solved Example Problems | Statistics , 11th Statistics : Chapter 5 : Measures of Central Tendency

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11th Statistics : Chapter 5 : Measures of Central Tendency : Partition Measures | Formula, Solved Example Problems | Statistics

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