3 Marks Question

Question 13 Marks

Find out the median of the data given below by arranging them in ascending order

X	160	150	152	161	156
Frequency	5	8	6	3	7

Answer

The given series is a discrete series. So after arranging the data in ascending order, we have to find the cumulative frequency i.e. c multiplied by f.
Calculation of Median

X	Frequency (f)	Cumulative Frequency (cf)
150	8	8
152	6	14
156	7	21
160	5	26
161	3	29
	$\Sigma f=29$

$\therefore M=$ Size of $\left(\frac{n+1}{2}\right)$ th item $=$ Size of $\left(\frac{29+1}{2}\right)$ th item
$=$ Size of $15^{\text {th }}$ item
Since 15 is greater than 14 and less than 21 , so, the 15 th item lies in cf 21 , and the value corresponding to this cumulative frequency is 156 .
Hence Median =156

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Question 23 Marks

Calculate the weighted mean of the following distribution.

Items	12	29	14	41
Weight	6	4	5	2

Answer

For calculating the weighted mean, we have to multiply each item of the series by its weights, i.e. X has to be multiplied by W and then we have to find the total of XW i.e. . ΣXW

Calculation of Weighted Mean

X	W	XW
12	6	72
29	4	116
14	5	70
41	2	82
	$\Sigma W=17$	$\Sigma X W=340$

Weighted mean $=\bar{X}_W=\frac{\Sigma X W}{\Sigma W}=\frac{340}{17}=20$
Thus, $\bar{X}_W=20$

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Question 33 Marks

Explain four limitations of consumer price index numbers.

Answer

1. Errors may occur in the construction because of inaccurate specification of groups for whom the index is meant.
2. Faulty selection of representative commodities resulting out of unscientific family budget enquiries.
3. Inadequate and unrepresentative nature of price quotations and use of inaccurate weights.
4. Frequent changes in demand and prices of the commodity. The average family might not be always a representative one.

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