4 Marks Question

Question 14 Marks

Mr. X is conducting a survey in his locality to understand proportion of rich and poor persons in his locality. Due to lack of time, he did not cover a part of his locality and took certain assumptions for the data. Do you think he did the right thing?

Answer

Mr. X did not follow the value of accuracy as his data cannot be complete without coverage of the whole of locality. He should not take assumptions as that will render his data collection exercise inaccurate

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Question 24 Marks

Direction of export is shown in the following table. Prepare a pie diagram to show the percentage distribution of export.

Country	Export (in %)
USA	25
Japan	15
UK	30
China	20
Others	10

Answer

For constructing a pie diagram, it is necessary to convert the percentage into corresponding degrees in the circle. Since one circle contains 360 degrees, therefore we calculate the degree of angles by multiplying the percentage value by 3.6 i.e. $\frac{360}{100}$ which is equal to 3.6. The conversion to degree of angles is shown in the following table.

Country	Percentage of Export	Degree of Angles
USA	25	$\frac{25}{100} \times 360^{\circ}=90^{\circ}$
Japan	15	$\frac{15}{100} \times 360^{\circ}=54^{\circ}$
UK	30	$\frac{30}{100} \times 360^{\circ}=108^{\circ}$
China	20	$\frac{20}{100} \times 360^{\circ}=72^{\circ}$
Others	10	$\frac{10}{100} \times 360^{\circ}=36^{\circ}$
	100	$360^{\circ}$

A pie diagram to show percentage distribution export is given below :

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Question 34 Marks

Draw the ‘less-than’ and ‘more-than’ ogive from the data given below

Weekly Wages (in Rs.)	Number of Workers
0-20	10
20-40	20
40-60	40
60-80	20
80-100	10

Answer

For less-than and more-than ogives, we will have to prepare less-than and more-than frequency distributions.
In less than method, the frequencies of all the preceding class intervals are added to the frequency of a class.
In more than method, the frequencies of all the succeeding class intervals are added to the frequency of a class.
The computation for both less than and more than ogive is given in the following table.

Less-than Distribution		More-than Distribution
Weekly Wages (in Rs.)	Number of Workers	Weekly Wages (in Rs.)	Number of Workers
Less than 20	10	More than 0	100
Less than 40	30	More than 20	90
Less than 60	70	More than 40	70
Less than 80	90	More than 60	30
Less than 100	100	More than 80	10

The less-than’ and ‘more-than ogives of the given data are shown below

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Question 44 Marks

Convert the following inclusive class interval into exclusive class interval.

Inclusive Class Interval	Frequency (f)
0-99	2
100-199	4
200-299	5
300-399	6
400-499	3
500-599	5
Total	25

Answer

To convert the inclusive series into exclusive series
Correction factor = 100-99 /2=0.5
This is added to the upper limit and subtracted from the lower limit of the class.
The exclusive class interval table of a given form is shown below

Inclusive Class Interval	Frequency (f)
0-99.5	2
99.5-199.5	4
199.5-299.5	5
299.5-399.5	6
399.5-499.5	3
499.5-599.5	5
Total	25

In this case, as the lower limit of first class is zero, hence 0.5 will not be subtracted from it.

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