The following data gives the placement statistics for a college. The annual salaries of 100 students (in lakhs) are tabulated along with the number of students in each salary bracket. Find the quartile deviation of the data to the nearest integer.

$\begin{matrix} S a l a r y B r a c k e t (i n l p a) & 0 - 5 & 5 - 10 & 10 - 15 & 15 - 20 & 20 - 25 & 25 - 30 N o . o f s t u d e n t s & 38 & 24 & 20 & 9 & 6 & 3 \end{matrix}$

4 lakhs

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5 lakhs

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6 lakhs

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7 lakhs

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Solution

The correct option is B
5 lakhs

$\begin{matrix} C l a s s I n t e r v a l & F r e q u e n c y & C u m u l a t i v e F r e q u e n c y 0 - 5 & 38 & 38 5 - 10 & 24 & 62 10 - 15 & 20 & 82 15 - 20 & 9 & 91 20 - 25 & 6 & 97 25 - 30 & 3 & 100 \end{matrix}$

$\frac{N}{4} = 25$

Therefore, class corresponding to the first quartile is 0-5

$Q_{1} = L + \frac{\frac{N}{4} - c . f}{f} \times h = 0 + \frac{25 - 0}{38} \times 5 = 3.29 l p a$

$\frac{3 N}{4} = 75$

Therefore, class corresponding to the third quartile is 10-15

$Q_{3} = L + \frac{\frac{3 N}{4} - c . f}{f} \times h = 10 + \frac{75 - 62}{20} \times 5 = 13.25 l p a$

$Q u a r t i l e D e v i a t i o n = \frac{Q_{3} - Q_{1}}{2} = \frac{13.25 - 3.29}{2} = 4.98$

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Similar questions

The following data gives the placement statistics for a college. The annual salaries of 100 students (in lakhs) are tabulated along with the number of students in each salary bracket. You want to find the salary of a typical student, ignoring the extreme values. Identify the measure of central tendency appropriate for this purpose and calculate it.

$\begin{matrix} S a l a r y B r a c k e t (i n l p a) & 0 - 5 & 5 - 10 & 10 - 15 & 15 - 20 & 20 - 25 & 25 - 30 N o . o f s t u d e n t s & 38 & 24 & 20 & 9 & 6 & 3 \end{matrix}$

The median class for the following data is
$\begin{matrix} M a r k s & B e l o w 10 & B e l o w 20 & B e l o w 30 & B e l o w 40 & B e l o w 50 N o . o f s t u d e n t s (c f) & 5 & 10 & 23 & 31 & 40 \end{matrix}$

The following data gives marks obtained by students in an exam.

$\begin{matrix} M a r k s & N o . o f s t u d e n t s A b o v e 0 & 80 A b o v e 10 & 77 A b o v e 20 & 72 A b o v e 30 & 65 A b o v e 40 & 55 A b o v e 50 & 43 A b o v e 60 & 23 A b o v e 70 & 16 A b o v e 80 & 10 A b o v e 90 & 8 A b o v e 100 & 0 \end{matrix}$

(i) Convert to a regular distribution.

(ii) Find the mode. [3 MARKS]

199 students were asked how many hours they exercise each week.

The following table shows the data :

$\begin{matrix} Time(t hours) & No. of students 0 - 5 & 12 5 - 10 & 15 10 - 15 & 23 15 - 20 & 30 20 - 25 & 40 25 - 30 & 35 30 - 35 & 25 35 - 40 & 20 \end{matrix}$

Find the Median of the data.

Q. Calculate the Quartile Deviation and Coefficient of Quartile Deviation of the following data:

Marks	:	5-9	10-14	15-19	20-24	25-29	30-34	35-39
Students	:	1	3	8	5	4	2	2

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