Quartile
Quartile
A quartile is the variate value which divides the value of given frequency into four equal parts. There are three quartiles, they are: 
 Lower Quartile (Q_{1})
 Middle Quartile (Q_{2})
 Upper Quartile (Q_{3})
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 (Q_{1}) = value of (\(\frac{N+1}{4}\))^{th}item.
Upper Quartile (Q_{3}) =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 (Q_{1}) = value of (\(\frac{N+1}{4}\))^{th}item
Upper quartile (Q_{3}) = 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 (Q_{1}) = 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 (Q_{3}) = 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

In the data set below, what is the lower quartile?
1, 2, 4, 4, 5, 6, 6, 6, 7, 7, 8
4
2
6
7

In the data set below, what is the upper quartile?
1, 2. 4, 4, 5, 6, 6, 6 , 7, 7, 8
6
5
8
7

In the data set below, what is the lower quartile?
29, 34, 38, 41, 51, 57, 65, 65, 81, 83
41
29
38
34

In the data set below, what is the upper quartile?
17, 23, 32, 36, 52, 54, 67, 83, 98, 99
67
99
83
98

In the data set below, what is the lower quartile?
2, 2, 2, 2, 3 , 5, 5, 5, 7, 8, 9, 95
3
2
7

In the data set below, what is the upper quartile?
2, 2, 2, 2, 3 , 5, 5, 5, 7, 8, 9, 97
9
8
5

In the data set below, what is the upper quartile?
20, 38, 52, 54, 60, 87, 93
54
93
87
60

In the data set below, what is the lower quartile?
10, 27, 27, 29, 44, 672744
27
10
29

In the data set below, what is the lower quartile?
19, 37, 41, 43, 83, 85, 94
43
85
37
19

In the data set below, what is the upper quartile?
19, 37, 41, 43, 83, 85, 94
43
94
85
83

In the data set below, what is the lower quartile?
23, 26, 26, 30, 34, 42, 49, 60, 96, 96, 96
32
34
26
30

In the data set below, what is the upper quartile?
59, 86, 86, 88, 96, 9686
59
88
96

In the data set below, what is the lower quartile?
2, 4, 5, 6, 6, 7, 8, 8, 8, 9
6
5
4
2

In the data set below, what is the upper quartile?
2, 4, 5, 6, 6, 7, 8, 8, 8, 9
7
8
9
6

In the data set below, what is the upper quartile?
1, 1, 1, 2, 2, 4, 4, 5, 5, 6
4
5
6
1

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