3 Marks Question

Question 13 Marks

Find unknown frequency in the table given below.

X	Frequency (f)
5	5
10	7
15	?
20	10
25	8
30	6
	$\Sigma f=50$

Answer

To find unknown frequency subtract the sum of known frequencies from the sum of total frequencies. Here it is given that the sum of frequencies is 50 .
$\Sigma f=50$
and the known frequencies are $5,7,10,8$ and 6.
$\because$ Sum of known frequency $=5+7+10+8+6=36$
$\therefore$ Unknown Frequency $=$ Total Frequency-Sum of Known Frequencies
$=50-36=14 .$
Therefore, the missing frequency is 14 .

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Question 23 Marks

The sales of a balloon seller in seven days of a week are as given below.

Days	Mon	Tue	Wed	Thu	Fri	Sat	Sun
Sales (in Rs.)	100	150	125	140	160	200	250

If the profit is 20% of sales, then find his average profit per day.

Answer

We can find the profit of each day by using the formula $P=\frac{20}{100} \times$ sales

Days	Mon	Tue	Wed	Thu	Fri	Sat	Sun
Profit (P) (in Rs.)	20	30	25	28	32	40	50

Mean $=$ Sum of all observations $/$ Total no. of observations $=\frac{\Sigma P}{n}$
Here, total no. of observations $=7$.
$\begin{array}{l}
\text { Average Profit }(\bar{P})=\frac{20+30+25+28+32+40+50}{7} \\
=\frac{225}{7}=\text { Rs } 32.14
\end{array}$

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Question 33 Marks

For a data Lasperey's index number is 120 and fisher's index number is 125. Calculate Paasche's index number.

Answer

Fisher's Index $=\sqrt{\frac{\sum_{P_{190}} \sum_{P_{1 q_1}}}{\sum_{P_{090}} \sum_{P_{0 q 1}}}}$
Fisher's Index $=\sqrt{L \times P}$
$125=\sqrt{120 \times P}$
On squaring both sides;
$\begin{array}{l}
15625=120 \times P \\
\frac{15625}{120}=P \\
P=130.21
\end{array}$

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