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 (\(\frac{N+1}{4}\))^th item.

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 (\(\frac{N+1}{4}\))^th item

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