CBSE NCERT Class XI (11th)  Economics
Ncert Solutions of Statistics for Economics for Chapter 4 : Presentation of Data
Q1 :
Bar diagram is a
(i) onedimensional diagram
(ii) twodimensional diagram
(iii) diagram with no dimension
(iv) none of the above
Answer :
Bar diagrams are Onedimensional diagrams. These are
represented on a plane of two axis and depicts the relationship between the two
variables (plotted on the either axis) in form of rectangular bars.
Q2 :
Data represented through a histogram can help in finding
graphically the
(i) mean
(ii) mode
(iii) median
(iv) all the above
Answer :
Graphically mode can be determined by presenting the data in
the form of Histogram. The highest Histogram indicates the modal class. The
intersection point of the lines diagonally joining the two top corners of the
modal rectangles to the corners of the adjacent Histograms indicates the Modal
Value.
Q3 :
Ogives can be helpful in locating graphically the
(i) mode
(ii) mean
(iii) median
(iv) none of the above
Answer :
Graphically, Median can be determined by the intersection
point of Less than Ogive and More than Ogive. The value of xaxis
corresponding to the intersection point indicates the median.
Q4 :
Data represented through arithmetic line graph help in
understanding
(i) longterm trend
(ii) cyclicity in data
(iii) seasonality in data
(iv) all the above
Answer :
Data represented through arithmetic line graph (or time
series graph) helps in understanding the longterm trend and periodicity.
Q5 :
Width of bars in a bar diagram need not be equal
(True/False).
Answer :
The above statement is false as all bars in a bar diagram
need to be of equal width. Moreover, all bars are at equal distance from each
other.
Q6 :
Width of rectangles in a histogram should essentially be
equal (True/False).
Answer :
The above statement is false, as the width of all rectangles
in a histogram may or may not be equal. The width of a rectangle depends on the
width of its corresponding class interval.
Q7 :
Histogram can only be formed with continuous
classification of data (True/False).
Answer :
Yes, a Histogram can only be formed with the continuous
classification of data. The frequency distribution of a continuous series is
graphically presented in form of a Histogram. If the given data is not
continuous, then it is to be converted into exclusive series before presenting
the data in the form of Histogram. Histograms can never be prepared for
discrete series.
Q8 :
Histogram and column diagram are the same method of presentation
of data (True/False).
Answer :
The above statement is false. This is because Histogram and
column diagram are different method of presentation. While the Histogram is a
Twodimensional diagram, the bar diagram is a Onedimensional diagram. Histograms
are prepared for the continuous series, whereas the bar diagrams are prepared
for the discrete series. Further, Histograms are drawn continuously without any
space between two consecutive Histograms, whereas the space is must between two
bars in a bar diagram.
Q9 :
Mode of a frequency distribution can be known graphically
with the help of histogram (True/False).
Answer :
The above statement is true. Graphically, mode can be
determined by presenting the data in the form of Histogram. The highest Histogram
indicates the modal class. The intersection point of the lines diagonally
joining the two top corners of the modal rectangles to the corners of the
adjacent Histograms indicates the Modal Value.
Q10 :
Median of a frequency distribution cannot be known from
the ogives (True/False).
Answer :
The statement is false. Graphically Ogives can be determined
by the intersection point of the less than Ogive and more than Ogive. The value
of xaxis corresponding to the intersection point indicates the median.
Q11 :
What kinds of diagrams are more effective in representing
the following?
(i) Monthly rainfall in a year
(ii) Composition of the population of Delhi by religion
(iii) Components of cost in a factory
Answer :
(i) The monthly rainfall in a year can be best represented
by a bar diagram as only one variable i.e. monthly rainfall is to be compared
visually. The highest bar diagram indicates the highest rainfall in the
corresponding month that is plotted on the xaxis.
(ii) Composition of the population of Delhi by religion can
be represented by a simple bar diagram. Plotting different religion on the
xaxis and the number of people on the yaxis, one can easily compare the
number of the population religionwise..
(iii) In order to represent different components of cost in
a factory, a pie chart is more effective. The entire circle represents the
total cost and various components of costsare shown by different portions of
the circle.
Q12 :
Suppose you want to emphasise the increase in the share
of urban nonworkers and lower level of urbanisation in India as shown in
Example 4.2. How would you do it in the tabular form?
Answer :
Share of Rural and Urban Nonworkers in India


Nonworkers in Urban

Nonworkers in Rural

Total Nonworkers Population

(1)

(2)

(3) = (1) + (2)

19,31,38,837

42,96,00,032

62,27,38,869

Source: Census of India, 2001
We can infer from the above table that the absolute number
of the rural nonworkers is greater than the absolute number of the urban
nonworkers. The higher ( lower) share of the rural nonworkers (urban
nonworkers) reveals lower degree of urbanisation in India.
NOTE: As there is no Example 4.2 in the book, so
the following data have been adapted from Census of India, 2001.
Q13 :
How does the procedure of drawing a histogram differ when
class intervals are unequal in comparison to equal class intervals in a
frequency table?
Answer :
A Histogram of equal class intervals has equal width of all
rectangles indicating the same class intervals. In contrast, a Histogram of
unequal class intervals has rectangles of varying width as per their
corresponding class intervals. Before constructing a Histogram, frequencies of
unequal class intervals are to be adjusted. The adjustment factor of each class
is calculated with the following formula.
And the adjusted frequency will be calculated by dividing
the original frequency by adjustment factor.
Q14 :
The Indian Sugar Mills Association reported that, 'Sugar
production during the first fortnight of December 2001 was about 3,87,000
tonnes, as against 3,78,000 tonnes during the same fortnight last year (2000).
The offtake of sugar from factories during the first fortnight of December
2001 was 2,83,000 tonnes for internal consumption and 41,000 tonnes for exports
as against 1,54,000 tonnes for internal consumption and nil for exports during
the same fortnight last season.'
(i) Present the data in tabular form.
(ii) Suppose you were to present these data in
diagrammatic form which
of the diagrams would you use and why?
(iii) Present these data diagrammatically.
Answer :
(i)
Sugar Production in India


Month, Year

Total Production

Internal Consumption

Export of Sugar

(tonnes)

(tonnes)

(tonnes)


Dec, 2000

3,78,000

1,54,000



Q15 :
The following table shows the estimated sectoral real
growth rates
(percentage change over the previous year) in GDP at
factor cost.
Year

Agriculture and allied sectors

Industry

Answer :