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ICSE Guess > ICSE/ISC eBooks > Class X > Maths by Mr. M. P. Keshari

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Example – 3. Calculate the lower and upper quartiles, inter quartile range and semi inter quartile range for the following distribution :

Class	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50	50 – 60	60 – 70	70 – 80
Frequency	2	4	20	32	18	15	5	4

Solution :- At first we prepare cumulative frequency table as follows :

Class-interval	Frequency	Cumulative frequency (cf)
0 – 10	2	2
10 – 20	4	6
20 – 30	20	26
30 – 40	32	58
40 – 50	18	76
50 – 60	15	91
60 – 70	5	96
70 – 80	4	100

Here, n/4 = 100/4 = 25, L₁ = 20, i₁ = 10, f₁ = 20, cf = 6.
                    Q₁ = L₁ + (i₁/f₁)(n/4 – cf )
                          = 20 + (10/20)(25 – 6 )
                          = 20 + 19/2 = 29.5.

Also, 3n/4 = 3×100/4 = 75, L₂ = 40, i₂ = 10, f₂ = 18, cf = 58.
                     Q₂ = L₂ + (i₂/f₂)(3n/4 – cf )
                           = 40 + (10/18)(75 - 58)
                           = 40 + 170/18 = 49.44.

Calculation of quartiles by Ogive.

For this we draw an ogive and then take a point corresponding to n/4 for lower quartile and 3n/4 for upper quartile. The foot of perpendicular of these points on x-axis will give the lower and upper quartile respectively.