Questions

4 Marks Question

Take a timed test

4 questions · self-marked practice — reveal the answer and mark yourself.

Question 14 Marks
Explain law of statistical regularity and law of inertia of large numbers in short.
Answer
1. Law of statistical regularity: This law is formulated on the theory of probability. According to this law, if a random sample of adequate size is selected from a large population, it tends to possess the same characteristics as those of the population. It implies that a sample can give an approximately equal value of entre population if sample is selected at random. For example, if 100 girls are selected form a group of 1000 and their heights are taken then average height obtained will be approximately equal to average height obtained by sum of 5000 girls.
2. Law of inertia of large numbers: This law is a corollary to law of statistical regularity. It states that the averages obtained from a large number are more stable than the aggregates or averages obtained from a small number. If a coin is tossed 10 times it is possible that one gets 9 heads and one tail but if it is tossed 1000 times, figure will be nearer to 500 for both.
View full question & answer
Question 24 Marks
Briefly discuss important guidelines while constructing graphs.
Answer
The following general guidelines are taken into consideration while preparing graphs:
1. Title: Each graph should have a suitable title. It may be given either at the top of the graph or below it. The title must convey the main the me which the graph intends to portray.
2. Size: The size and portion of each component of a graph should be such that all the relevant characteristics of the data are properly displayed and can be· easily understood.
3. Proportion of length and breadth: An appropriate proportion between the length and breadth of the graph should be maintained. As such there are no fixed rules about the ratio of length to width.
4. Proper scale: There are again no fixed rules for selection of scale. The graph should neither be too small nor too large. The scale for the graph should be decided after taking into consideration the magnitude of data and the size of the paper on which it is to be drawn. The scale showing the values as far as possible should be in even numbers or in multiples of 5, 10, 20, and so on. The scale should specify the size of the unit and the nature of data it represents, for example, 'millions of tone’s', in Rs. thousand, and the like. The scale adopted should be indicated on both vertical and horizontal axes if different scales are used. Otherwise, it can be indicated at some suitable place on the graph paper.
5. Footnotes and source note: To clarify or elucidate any points which need further explanation but cannot be shown in the graph, footnotes are given at the bottom of the graphs. 6. Index: A brief index explaining the different types of lines, shades, designs, or colours used in the construction of the graph should be given to understand its contents.
6. Simplicity: Graphs should be prepared in such a way that they can be understood easily. To keep it simple, too much information should not be loaded in a single graph as it may create confusion. Thus if the data are large, then it is advisable to prepare more than one graph, each depicting some identified characteristic of the same data.
View full question & answer
Question 34 Marks

The following data shows the number of cars manufactured by Maruti Ltd, Tata Motors and Hyundai in the year 2015-16. Represent it with the help of a piediagram.


Production of Cars (in Rs.)

Maruti Limited

15,75,000

Tata Motors

7,25,000

Hyundai

5,50,000

Answer
Name of the CompanyProductionpercentage valuesAngle (in degree)
Maruti Limited15,75,000$\frac{15,75,000}{28,50,000} \times 100=55.26$$\frac{55.26 \times 360}{100}=199^{\circ}$
Tata Motors7,25,000$\frac{7,25,000}{28,50,000} \times 100=25.43$$\frac{25.43 \times 360}{100}=92^{\circ}$
Hyundai5,50,000$\frac{5,50,000}{28,50,000} \times 100=19.3$$\frac{19.3 \times 360}{100}=-69^{\circ}$
Total28,50,000 $360^{\circ}$
In the above table, we have calculated the percentage values of the production figures first and then we have computed the angle in degrees for each value. The pie diagram for the above data is given below:
Image
View full question & answer
Question 44 Marks
Convert the following inclusive series into exclusive series.
Class Interval1-56-1011-1516-2021-25
Number of Workers1015202530
Answer
 To convert the inclusive series into exclusive series we need to find correction factor = 6 -5 /2=0.5
This is added to the upper limit and subtracted from the lower limit of the class.
The exclusive series of the given inclusive series is shown below
Class IntervalFrequency (f)
0.5-5.510
5.5-10.515
10.5-15.520
15.5-20.525
20.5-25.530
Total100
View full question & answer