Find the quartile deviation of advertisement expenditure using fo… - Vidyadip

Question

Find the quartile deviation of advertisement expenditure using following frequency distribution of advertising expenditure of $50$ companies :

Advertisement cost (thousand $Rs$. )	$0 – 5$	$5 – 15$	$15 – 30$	$30 – 40$	$40 – 60$	$60 -100$	Total
No. of companies	$3$	$8$	$15$	$10$	$8$	$6$	$50$

✓

Answer

Expenditure of advertisement (thousand $Rs.$ )	No. of companies $f$	Cumulative frequency $cf$
$0 – 5$	$3$	$3$
$5 – 15$	$8$	$11$
$15 – 30$	$15$	$26$
$30 – 40$	$10$	$36$
$40 – 60$	$8$	$44$
$60 – 100$	$6$	$50$
Total	$n = 50$

First quartile :
$Q _1$ class $=$ class that includes $\left(\frac{n}{4}\right)$ th observation
$=$ class that includes $\left(\frac{50}{4}\right)$
$=12.5$ th observation
Referring to column cf, $Q_1$ class $=15-30$
Now, $Q_1=L+\frac{\left(\frac{n}{4}\right)-c t}{f} X c$
Putting $L=15, \frac{n}{4}=12.5$, $cf$ $=11, f=15$ and $c=15$ in the formula, $Q _1=15+\frac{12.5-11}{15} \times 15$
$=15+1.5=$ $Rs 16.5$ thousand
Third quartile :
$Q _3$ Class $=$ Class that includes $3\left(\frac{n}{4}\right)$ th observation
$=$ Class that includes $3(12.5)$
$=37.5$ th observation
Referring to column cf, $Q_3$ class $=40-60$
Now, $Q _3=L+\frac{3\left(\frac{n}{4}\right)- cf }{f} \times c$
Putting, $L=40,3\left(\frac{n}{4}\right)=37.5, c f=36, f=8$ and $c=20$ in the formula, $Q _3=40+\frac{37.5-36}{8} \times 20=40+\frac{1.5 \times 20}{8}=40+\frac{30}{8}=40+3.75=$ $Rs. 43.75$ thousand
Quartile deviation :
$Q _{ d }=\frac{Q 3-Q 1}{2}=\frac{43.75-16.5}{2}=\frac{27.5}{2}=13.625 \approx 13.63 \text { thousand }$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "4 Marks Each" from Measures of dispersion→Measures of dispersion — all question types→Statistics STD 11 Commerce question papers→Gujarat Board STD 11 Commerce question papers→Gujarat Board question paper generator→

Similar questions

There were $1400$ students studying in a commerce college. Among them, $855$ were boys and of them, $225$ boys were in the second year. In the second year, the number of boys and the number of girls are equal. Among the $550$ students of the first year, the proportion of number of boys and the girls is $3:2$. In the third year, number of boys is three times the number of girls. Represent the above information in a table.

In a housing scheme a customer has to pay the cost of a house in $20$ annual instalments. He has to pay $Rs. 1000$ in the first instalment and there after he has to pay double amount of the previous instalment. How much amount will he pay in $10th$ yearly?

Discuss the characteristics of an ideal questionnaire.

If the fourth term and the seventh term are $\frac{3}{4}$ and $\frac{3}{32}$ respectively for a $G.P.,$ find its tenth term.

Define skewed frequency distribution and state its characteristics.

From the following information of fortnight sale of two wheelers by $30$ dealers of a city, ﬁnd the mean deviation of ‘number of two wheelers sold’.

The information about marks of students from two commerce classes of standard $11$ of a school is as follows. Find the coefficient of skewness by Karl Pearson's and Bowley's method.

Weight (kg)	65	60	54	52	50	48	46	45
No. of persons	2	5	7	8	6	4	5	3

In how many ways can $5$ boys and $2$ girls be arranged in a row such that,
$(1)$ both the girls are together ?
$(2)$ both the girls are not together ?

Discuss what types of precautions should be taken while using secondary data.

Represent the following data in an appropriate table. $800$ candidates appeared for a public examination. Of these candidates, the number of boys exceeded number of girls by $20 \%$ of the total candidates. The number of candidates passed exceeded the number of candidates failed by $420$ . The number of boys failed were $130$ .