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Question-1

Suppose you want to emphasise the increase in the share of urban non-workers and lower level of urbanisation in India as shown in Example 4.2. How would you do it in the tabular form?

Solution:

 

 

Year

Urban non-workers

Percentage

1995

1996

1997

1998

1999

2000

43100

48820

52917

60035

65220

74463

12.50

14.17

15.35

17.42

18.93

21.61

All

344555

100.00

 

 

 

 

Question-2

How does the procedure of drawing a histogram differ when class intervals are unequal in comparison to equal class intervals in a frequency table?

Solution:
When the class intervals are equal, then by the usual method, we can draw a histogram.

When the class intervals are unequal, then make intervals into True class intervals and then by the usual method, we can draw a histogram.

Question-3

(iii) Present these data diagrammatically.

 


Solution:

(i)

 

In tonnes

2000 (in lakhs)

2001 (in lakhs)

Sugar production

3.78

3.87

Internal consumption

1.54

2.83

Exports

--

0.41

 

 

(ii) Sub-divided bar diagram

(iii) Here, unit for x-axis is in years and unit for y-axis is in lakhs.

Question-4

Represent the data as multiple time series graphs.

 


Solution:

Question-5

How to make a statistical table? And explain its parts in brief:

Solution:
The simplest way of conceptualising a table may be data presented in rows and columns along with some explanatory notes. Tabulation can be done using one-way, two-way or three-way classification depending upon the number of characteristics involved. A good table should essentially have the following:

 

(i) Table Number

Table number is assigned to a table for identification purpose. If more than one table is presented, it is the table number that distinguishes one table from another. It is given at the top or at the beginning of the title of the table. Generally, table numbers are whole numbers in ascending order if there are many tables in a book. Subscripted numbers like 1.2, 3.1, etc. are also in use for identifying the table according to its location.

 

(ii) Title

The title of a table narrates about the contents of the table. It has to be very clear, brief and carefully worded so that the interpretations made from the table are clear and free from any ambiguity. It finds place at the head of the table succeeding the table number or just below it.

 

(iii) Captions or Column Headings

At the top of each column in a table a column designation is given to explain figures of the column.

 

(iv) Stubs or Row Headings

Like a caption or column heading each row of the table has to be given a heading. The designations of the rows are also called stubs or stub items, and the complete left column is known as stub column.

 

(v) Body of the Table

Body of a table is the main part and it contains the actual data. Location of any one figure/data in the table is fixed and determined by the row and column of the table.

 

(vi) Unit of Measurement

The unit of measurement of the figures in the table (actual data) should always be stated along with the title if the unit does not change throughout the table. If different units are there for rows or columns of the table, these units must be stated along with ‘stubs’ or ‘captions’.

 

(vii) Source Note

It is a brief statement or phrase indicating the source of data presented in the table. If more than one source is there, all the sources are to be written in the source note. Source note is generally written at the bottom of the table.

 

(viii) Footnote

Footnote is the last part of the table. Footnote explains the specific feature of the data content of the table which is not self explanatory and has not been explained earlier.

Question-6

What is the use of diagrammatic presentation of data?

Solution:
This is the third method of presenting data. This method provides the quickest understanding of the actual situation to be explained by data in comparison to tabular or textual presentations. Diagrammatic presentation of data translates quite effectively the highly abstract ideas contained in numbers into more concrete and easily comprehensible form. Diagrams may be less accurate but are much more effective than tables in presenting the data.

There are various kinds of diagrams in common use. Amongst them the important ones are the following:

(i) Geometric diagram

(ii) Frequency diagram

(iii) Arithmetic line graph

Question-7

What is mean by Histogram?

Solution:
A histogram is a two dimensional diagram. It is a set of rectangles with bases as the intervals between class boundaries (along X-axis) and with areas proportional to the class frequency (Fig.4.5).
 

If the class intervals are of equal width, which they generally are, the area of the rectangles are proportional to their respective frequencies. However, in some type of data, it is convenient, at times necessary, to use varying width of class intervals.
 

For example, when tabulating deaths by age at death, it would be very meaningful as well as useful too to have very short age intervals (0, 1, 2, ..., yrs/ 0, 7, 28, ..., days) at the beginning when death rates are very high compared to deaths at most other higher age segments of the population.
 

For graphical representation of such data, height for area of a rectangle is the quotient of height (here frequency) and base (here width of the class interval). When intervals are equal, that is, when all rectangles have the same base, area can conveniently be represented by the frequency of any interval for purposes of comparison.
 

When bases vary in their width, the heights of rectangles are to be adjusted to yield comparable measurements. The answer in such a situation is frequency density (class frequency divided by width of the class interval) instead of absolute frequency.

 

Question-8

What are the different forms of presentation?

Solution:
Textual, Tabular and Diagrammatic are the three forms of presentations.

Question-9

What is mean by an Arithmetic line graph? And what is the use of it?

Solution:
An arithmetic line graph is also called time series graph and is a method of diagrammatic presentation of data. In it, time (hour, day/date, week, month, year, etc.) is plotted along x-axis and the value of the variable (time series data) along y-axis. A line graph by joining these plotted points, thus, obtained is called arithmetic line graph (time series graph).

It uses in understanding the trend, periodicity, etc. in a long term time series data.

Question-10

How will you draw a frequency curve?

Solution:
The frequency curve is obtained by drawing a smooth free hand curve passing through the points of the frequency polygon as closely as possible.

It may not necessarily pass through all the points of the frequency polygon but it passes through them as closely as possible.

Question-11

How to transform a component bar diagram?

Solution:
A component bar diagram can be transformed into a Pie diagram.

Question-12

What is mean by a frequency polygon?

Solution:
A frequency polygon is a plane bounded by straight lines.

Question-13

How do you call ogive?

Solution:
Ogive is also called cumulative frequency curve.

Question-14

What is the use of drawing less than and more than ogive graphs?

Solution:
We can get Median of the data.

Question-15

How many ways of tabulation can be done and what are they?

Solution:
There are three ways of tabulation can be done and they are one-way, two-way and three-way classifications.

Question-16

(iii) Components of cost in a factory

 


Solution:
(i) Bar diagram

(ii) Pie diagram

(iii) Component Bar diagram or Pie diagram





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