6 Marks Question

Question 16 Marks

Compute mode from the following data.

Score	Frequency
0-10	10
10-20	20
20-30	18
30-40	32
40-50	21

Answer

Steps to be followed to calculate the Mode are:
1. Create a table with two columns
2. In column 1 write your class intervals
3. In column 2 write the corresponding frequencies
4. Locate the maximum frequency denoted by $f_m$
5. Determine the class corresponding to $f _{ m }$ this will be your Modal class
6. Calculate the Mode using given formula: $M_o=l_1+\frac{f_1-f_0}{2 f_1-f_0-f_2} \times c$

Calculation of mode

Score	Frequency
0-10	10
10-20	20
20-30	18
30-40	32
40-50	21

By observation method, it is clear that the modal value lies in the group of $30-40$ because it has the highest frequency.
$\begin{array}{l}
\therefore l_1=30, f_0=18, f_1=32, f_2=21 \text { and } c=10 \\
\text { Now, Mode }=l_1+\frac{f_1-f_0}{2 f_1-f_0-f_2} \times c \\
=30+\frac{32-18}{2 \times 32-18-21} \times 10 \\
=30+\frac{14}{25} \times 10 \\
=30+5.6=35.6
\end{array}$
Hence, the modal value is 35.6 score.

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Question 26 Marks

Calculate Q₁ and Q₃ from the following table.

Wages (in Rs.)	Number of Workers
0-5	4
5-10	6
10-15	3
15-20	8
20-25	12
25-30	7

Answer

Wages	Number of Workers	Cumulative Frequency (cf)
0-5	4	4
5-10	6	10
10-15	3	13
15-20	8	21
20-25	12	33
25-30	7	40
	$n=\Sigma f=40$

Calculation of Q₁ and Q₃

Q₁	Q₃
First Quartile number $\left(q_1\right)=$Size of $\left(\frac{n}{4}\right) th$ item	Third Quartile number $\left( q _3\right)=$ Size of $\left(\frac{3 n}{4}\right)$ th item
$=\left(\frac{40}{4}\right)$ th item $=10$ th item 10th item will correspond to the class 5-10. So, $l _1=5, cf =4, f =6$ and $c =5$ Now, $\begin{array}{l}Q_1=l_1+\frac{\frac{n}{4}-c f}{f} \times c=5 \\+\frac{10-4}{6} \times 5 \\5+\frac{6 \times 5}{6}=5+\frac{30}{6}=5+5 \\\Rightarrow Q_1=10\end{array}$	$=\left(\frac{3 \times 40}{4}\right)$ th item $=30$ th items 30th item will correspond to the class 20-25. So, $l _1=20, cf =21, f =12$ and $c =5$ Now, $Q_3=l_1+\frac{\frac{3 n}{4}-c f}{f} \times c=20$ $\begin{aligned} & +\frac{30-21}{12} \times 5 \\ = & 20+\frac{45}{12}=20+3.75 \Rightarrow Q_3 \\ = & 23.75 \end{aligned}$

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Question 36 Marks

Calculate the correlation coefficient between the height of fathers in inches (X) and their sons (Y).

X	65	66	57	67	68	69	70	72
Y	67	56	65	68	72	72	69	71

Answer

Calculation of Coefficient of Correlation

It indicates that there is low degree of positive correlation between height of fathers and sons.

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Economics 6 Marks Question

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