This page contains the NCERT Statistics for Economicsclass 11 chapter 4 Presentation of Data from the book Statistics for Economics. You can find the solutions for the chapter 4 of NCERT class 11 Statistics for Economics, for the Short Answer Questions, Long Answer Questions and Projects/Assignments Questions in this page. So is the case if you are looking for NCERT class 11 Statistics for Economics related topic Presentation of Data question and answers.
EXERCISES
Answer the following questions, 1 to 10, choosing the correct answer
1. Bar diagram is a
(i)
one-dimensional diagram ✔
(ii)
two-dimensional diagram
(iii)
diagram with no dimension
(iv)
none of the above
Bar diagram is a
–
Answer: (i) one-dimensional diagram.
–
Explanation: Although bar diagrams are represented on a plane with two axes, they are considered one-dimensional. This is because only the length of the bars is significant in representing data, while the width of the bars is of no consequence. The length of the bars depicts the frequency or magnitude of the data, making bar diagrams one-dimensional in their representation of information.
2. Data represented through a histogram can help in finding graphically the
(i)
mean
(ii)
mode ✔
(iii)
median
(iv)
all the above
Data represented through a histogram can help in finding graphically the
–
Answer: (ii) mode.
–
Explanation: Histograms are particularly useful for determining the mode of a set of data graphically.
3. Ogives can be helpful in locating graphically the
(i)
mode
(ii)
mean
(iii)
median ✔
(iv)
none of the above
Ogives can be helpful in locating graphically the
–
Answer: (iii) median.
–
Explanation: Ogives are cumulative frequency graphs used to find the median of a data set graphically. The intersection point of the “less than” and “more than” ogives represents the median.
4. Data represented through arithmetic line graph help in understanding
(i)
long term trend ✔
(ii)
cyclicity in data
(iii)
seasonality in data
(iv)
all the above
Data represented through arithmetic line graph help in understanding
–
Answer: (i) long term trend.
–
Explanation: Arithmetic line graphs, also known as time series graphs, are particularly useful for analyzing and understanding long-term trends in data. They plot a variable over time, allowing for a clear visualization of how the data evolves or changes over a longer period.
5. Width of bars in a bar diagram need not be equal (True/False ✔).
Width of bars in a bar diagram need not be equal
–
Answer: False.
–
Explanation: In a bar diagram, it is essential that all bars have equal width to ensure accurate representation and comparison of data. Additionally, bars in a bar diagram are typically spaced equally from each other. This uniformity in width and spacing is crucial for the clarity and effectiveness of a bar diagram in representing categorical or class data.
6. Width of rectangles in a histogram should essentially be equal (True/ False ✔).
Width of rectangles in a histogram should essentially be equal
–
Answer: False.
–
Explanation: In a histogram, the width of the rectangles (or bars) represents the class intervals of the data, and these intervals do not necessarily need to be of equal width. Histograms are used to represent the frequency distribution of continuous data, and the varying widths of the rectangles can correspond to different ranges in the data set. The area of each rectangle is proportional to the frequency of the observations in the interval it represents, allowing for varying widths while accurately depicting the data distribution.
7. Histogram can only be formed with continuous classification of data (True ✔/False).
Histogram can only be formed with continuous classification of data
–
Answer: True.
–
Explanation: Histograms are specifically designed for representing continuous data. They are used to illustrate the distribution of continuous variables by depicting the frequency of observations within different continuous intervals or ‘bins’. In a histogram, each bar represents an interval of values, and its height indicates the frequency of data points within that interval. This method of representation is not applicable for discrete or categorical data, which is why histograms are uniquely associated with continuous data classification.
8. Histogram and column diagram are the same method of presentation of data. (True/False ✔)
Histogram and column diagram are the same method of presentation of data
–
Answer: False.
–
Explanation: Histograms and column diagrams (or bar charts) are different methods of data presentation. A histogram is used for continuous data and represents the distribution of numerical data. The bars in a histogram touch each other, indicating the continuous nature of the data. On the other hand, a column diagram or bar chart is used for categorical or discrete data. The bars in a column diagram are separated by spaces, emphasizing the distinct categories or groups being compared. These differences in design and purpose distinguish histograms from column diagrams.
9. Mode of a frequency distribution can be known graphically with the help of histogram. (True ✔/False)
Mode of a frequency distribution can be known graphically with the help of histogram
–
Answer: True.
–
Explanation: A histogram can indeed be used to determine the mode of a frequency distribution graphically. The mode is the value that appears most frequently in a data set. In a histogram, this corresponds to the highest bar (or bars, in case of bimodal or multimodal distributions), as it represents the range of values with the highest frequency. Therefore, by identifying the peak or peaks in a histogram, one can visually determine the mode of the data.
10. Median of a frequency distribution cannot be known from the ogives. (True/False ✔)
Median of a frequency distribution cannot be known from the ogives
–
Answer: False.
–
Explanation: The median of a frequency distribution can indeed be determined using ogives. An ogive, or a cumulative frequency graph, comes in two types: the “less than” ogive and the “more than” ogive. When these two ogives are plotted on the same graph, the point where they intersect represents the median of the frequency distribution. This method is a graphical way of finding the median, especially useful for grouped data.
11. What kind 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
(i) Monthly Rainfall in a Year
–
Effective Diagram: Line Graph or Bar Graph.
–
Explanation: To represent monthly rainfall in a year, a line graph or a bar graph is most effective. A line graph shows the trend and fluctuations in rainfall over the months, making it easier to observe patterns, such as periods of high or low rainfall. Alternatively, a bar graph can effectively show the comparative amounts of rainfall each month.
(ii) Composition of the Population of Delhi by Religion
–
Effective Diagram: Pie Chart.
–
Explanation: A pie chart is most effective for representing the composition of a population by religion. It visually depicts the proportional distribution of different religious groups in Delhi, allowing for easy comparison of each group’s relative size to the total population.
(iii) Components of Cost in a Factory
–
Effective Diagram: Bar Graph or Pie Chart.
–
Explanation: Both a bar graph and a pie chart can effectively represent the components of cost in a factory. A bar graph can display the different cost components (like raw materials, labor, utilities, etc.) and their respective magnitudes, facilitating a comparison between them. A pie chart, on the other hand, shows the proportion of each cost component relative to the total cost, making it easy to see which components are the largest or smallest parts of the total cost.
12. 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?
The following is the summary of the data from Table 4.5 (Example 4.2, as given in the problem, is not available in the book) of the non-workers and total population in both urban and rural locations.
Location
Non-Workers (in Crores)
Total Population (in Crores)
Rural
43
74
Urban
19
28
Total
62
102
Share of Urban Non-Workers among the entire urban population can be calculaed as
{\dfrac{19}{28} × 100 = ≅ 68\%}
While, the share of Rural Non-Workers among the entire rural population can be calculaed as
{\dfrac{43}{74} × 100 = ≅ 58\%}
So, this can be represented in tabular format as
Location
Non-Workers
Non-Workers %
Rural
43
68
Urban
19
58
So, we cam emphasise that there is an increase in the share of urban non-workers (68% > 58%) and lower level of urbanisation (28 < 74) in India as shown in Example 4.2 Table 4.5.
13. How does the procedure of drawing a histogram differ when class intervals are unequal in comparison to equal class intervals in a frequency table?
Here’s a comparison of the procedure for drawing histograms with equal and unequal class intervals in a tabular format:
Aspect
Equal Class Intervals
Unequal Class Intervals
Scaling the Axes
Uniformly scaled x-axis for class intervals.
X-axis scaled according to varying class widths.
Bar Widths
All bars have the same width.
Width of each bar corresponds to class interval size.
Area Representation
Height of bars represents the frequency.
Area of bars represents the frequency; height is frequency divided by class width.
Visual Interpretation
Easier to visually compare frequencies.
Requires careful interpretation due to variable bar areas.
This table highlights the key differences in drawing histograms depending on whether the class intervals are equal or unequal, affecting scaling, bar widths, area representation, and visual interpretation.
14. 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 off-take 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.
(i) Tabular Presentation:
Year
Sugar Production (Tonnes)
Internal Consumption (Tonnes)
Exports (Tonnes)
2000
3,78,000
1,54,000
Nil
2001
3,87,000
2,83,000
41,000
(ii) Revised Choice of Diagrammatic Form:
A Multiple Bar Diagram would be a more effective way to present these data diagrammatically. The multiple bar diagram allows for a side-by-side comparison of different data sets (production, internal consumption, exports) for different years (2000 and 2001), making it easier to visualize and compare the changes over the two years.
(iii) Diagrammatic Presentation:
Comparative Analysis of Sugar Production, Internal Consumption, and Exports in December 2000 and 2001
15. 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
Services
1994–95
5.0
9.2
7.0
1995–96
–0.9
11.8
10.3
1996–97
9.6
6.0
7.1
1997–98
–1.9
5.9
9.0
1998–99
7.2
4.0
8.3
1999–2000
0.8
6.9
8.2
Represent the data as multiple time series graphs.
Multiple Time Series Line Graphs for GDP Growth rate from from 1994-2000