Find the inter-quartile range and coefficient of quartile deviation from the following data. | Statistics | SciPiPupil

Question: Find the inter-quartile range and coefficient of quartile deviation from the following data:

Weight (Kg)	10-20	10-30	10-40	10-50	10-60	10-70
No. of men	12	31	36	46	55	61

Solution:

Given,

Arranging the given data in cumulative frequency (c.f.) table:

Marks (x)	No. (f)	c.f.
10-20 (10-20)	12	12
10-30 (20-30)	19	31
10-40 (30-40)	5	36
10-50 (40-50)	10	46
10-60 (50-60)	9	55
10-70 (60-70)	6	61
	N=61

Now,

$Q_1 \; class = \dfrac{N}{4}^{th} \; class$

$= \dfrac{61}{4}^{th}\; class$

$= 15.25 ^{th} \; class$

In c.f. table, just greater value than 15.25 is 3@ whose corresponding class is (20-30). 

So, $Q_1\; class= (20-30)$

For $Q_1$ we have;

l = 20, i = 10, f = 19, c.f. = 12, $\frac{N}{4}$ = 15.25

So,

$Q_1 = l + \dfrac{i}{f} × \left ( \dfrac{N}{4} - c.f. \right )$

$= 20 + \dfrac{10}{19} × (15.25-12)$

$= 20 + 1.71$

$= 21.71$

And,

$Q_3 \; class = \dfrac{3N}{4}^{th} \; class$

$= \dfrac{3×61}{4}^{th}\; class$

$= 45.75 ^{th} \; class$

In c.f. table, just greater value than 45.75 is 46 whose corresponding class is (40-50). 

So, $Q_3\; class= (40-50)$

For $Q_3$ we have;

l = 40, i = 10, f = 10, c.f. = 36, $\frac{3N}{4}$ = 45.75

So,

$Q_3 = l + \dfrac{i}{f} × \left ( \dfrac{3N}{4} - c.f. \right )$

$= 40 + \dfrac{10}{10} × (45.75 - 36)$

$= 40 + 9.75$

$= 49.75$

We know,

Inter-quartile range = $Q_3 - Q_1$

$= 49.75 - 21.71$

$= 28.04$

Also,

Coefficient of Q.D. = $\dfrac{Q_3 - Q_1}{Q_3 + Q_1}$

$= \dfrac{49.75 - 21.71}{49.75+21.71}$

$= \dfrac{28.04}{71.46}$

$= 0.39$

Hence, the required inter-quartile range of the above data is 28.04 and the coefficient of quartile deviation is 0.39.

Related Notes and Solutions:

Here is the website link to the notes of Statistics of Class 10.

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