Quartile

A quartile is the variate value which divides the value of given frequency into four equal parts. There are three quartiles, they are: -

1. Lower Quartile (Q1)
2. Middle Quartile (Q2)
3. Upper Quartile (Q3)

Quartiles can be calculated as following ways: -

Individual series
After arranging the data in ascending order, the quartiles are calculated by applying the following formula:
Lower quartile (Q1) = value of ($$\frac{N+1}{4}$$)thitem.

Upper Quartile (Q3) =value of 3($$\frac{N+1}{4}$$)th item.

Where, N = Total sum of frequency.

Discrete Series
When the data are arranged in ascending order, the quartile is calculated by the following formula:
Lower quartile (Q1) = value of ($$\frac{N+1}{4}$$)thitem

Upper quartile (Q3) = value of 3($$\frac{N+1}{4}$$)th item

Where N = Total sum of frequency

Continuous Series
For continuous series, the following formulae area used.
Lower quartile class = value of 3($$\frac{N}{4}$$)th item

Exact Lower Quartile (Q1) = L + $$\frac{\frac{N}{4} - C.F}{f}$$× i
where,
L = Lower limit of corresponding class
f = frequency
c.f = cumulative frequency
i = class size
N = Total sum of frequency

Upper quartile class = value of 3($$\frac{N}{4}$$)th item

Exact upper quartile (Q3) = L + $$\frac{\frac{3N}{4} - C.F}{f}$$× i

• Quartile is the variate value which divides the value of given frequency into four equal parts.
• There are three quartiles, they are: lower quartile, middle quartile and upper quartile

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