Presentation of Data
NCERT Solutions • Class 11 Statistics • Chapter 4Objective Type Questions
1. Bar diagram is a:
(i) one-dimensional diagram
Reason: In a bar diagram, only the height (or length) of the bar matters. The width is arbitrary and does not represent any data value.
Reason: In a bar diagram, only the height (or length) of the bar matters. The width is arbitrary and does not represent any data value.
2. Data represented through a histogram can help in finding graphically the:
(ii) mode
Reason: The mode is located using the highest rectangle in a histogram.
Reason: The mode is located using the highest rectangle in a histogram.
3. Ogives can be helpful in locating graphically the:
(iii) median
Reason: The intersection point of the ‘Less than’ and ‘More than’ ogives corresponds to the median on the X-axis.
Reason: The intersection point of the ‘Less than’ and ‘More than’ ogives corresponds to the median on the X-axis.
4. Data represented through arithmetic line graph help in understanding:
(iv) all the above
Reason: Arithmetic line graphs (Time Series graphs) display long-term trends, cyclical movements, and seasonal variations over time.
Reason: Arithmetic line graphs (Time Series graphs) display long-term trends, cyclical movements, and seasonal variations over time.
5. Width of bars in a bar diagram need not be equal (True/False).
False.
Reason: In a standard bar diagram, bars should have equal width to ensure visual consistency and fair comparison, even though the width doesn’t represent data.
Reason: In a standard bar diagram, bars should have equal width to ensure visual consistency and fair comparison, even though the width doesn’t represent data.
6. Width of rectangles in a histogram should essentially be equal (True/False).
False.
Reason: While they *can* be equal, if class intervals are unequal, the widths of the rectangles will also be unequal. In such cases, we adjust the height (Frequency Density).
Reason: While they *can* be equal, if class intervals are unequal, the widths of the rectangles will also be unequal. In such cases, we adjust the height (Frequency Density).
7. Histogram can only be formed with continuous classification of data (True/False).
True.
Reason: Histograms represent continuous variables. If data is inclusive (with gaps), it must first be converted to exclusive (continuous) form.
Reason: Histograms represent continuous variables. If data is inclusive (with gaps), it must first be converted to exclusive (continuous) form.
8. Histogram and column diagram are the same method of presentation of data. (True/False)
False.
Reason: A column diagram (bar chart) has gaps between bars and represents discrete variables/attributes. A histogram has no gaps and represents continuous frequency distributions.
Reason: A column diagram (bar chart) has gaps between bars and represents discrete variables/attributes. A histogram has no gaps and represents continuous frequency distributions.
9. Mode of a frequency distribution can be known graphically with the help of histogram. (True/False)
True.
Reason: By drawing lines from the top corners of the highest bar to the adjacent bars, the modal value can be pinpointed on the X-axis.
Reason: By drawing lines from the top corners of the highest bar to the adjacent bars, the modal value can be pinpointed on the X-axis.
10. Median of a frequency distribution cannot be known from the ogives. (True/False)
False.
Reason: The Median *can* be determined graphically using Ogives (Cumulative Frequency Curves).
Reason: The Median *can* be determined graphically using Ogives (Cumulative Frequency Curves).
Descriptive Questions
11. What kind of diagrams are more effective in representing the following?
- (i) Monthly rainfall in a year: Simple Bar Diagram. (Effective for comparing distinct values over months).
- (ii) Composition of the population of Delhi by religion: Pie Diagram or Component Bar Diagram. (Best for showing parts of a whole).
- (iii) Components of cost in a factory: Sub-divided (Component) Bar Diagram or Pie Diagram. (Shows the breakdown of total cost into sub-parts).
12. Suppose you want to emphasise the increase in the share of urban non-workers and lower level of urbanisation in India… How would you do it in the tabular form?
To emphasize specific trends in a table, the following structure should be used:
Note: The table should clearly highlight the rising percentage of non-workers and the comparative urbanization figures to draw immediate attention to the relationship.
| Year | Distribution of Workers | Urbanisation Level (%) | |
|---|---|---|---|
| Total Urban Population | Share of Non-Workers (%) | ||
| Year 1 | … | … | … |
| Year 2 | … | … | … |
13. How does the procedure of drawing a histogram differ when class intervals are unequal in comparison to equal class intervals?
When class intervals are equal, the height of each rectangle corresponds directly to the frequency of that class.
When class intervals are unequal, frequencies cannot be plotted directly because it would distort the area representation. We must adjust the heights using Frequency Density:
$$ \text{Frequency Density} = \frac{\text{Class Frequency}}{\text{Width of Class Interval}} \times \text{Lowest Class Width} $$
The adjusted frequency is then plotted on the Y-axis.
When class intervals are unequal, frequencies cannot be plotted directly because it would distort the area representation. We must adjust the heights using Frequency Density:
$$ \text{Frequency Density} = \frac{\text{Class Frequency}}{\text{Width of Class Interval}} \times \text{Lowest Class Width} $$
The adjusted frequency is then plotted on the Y-axis.
Data Interpretation
14. Sugar Production Data (Indian Sugar Mills Association).
(i) Tabular Presentation:
(ii) Diagram Choice:
A Multiple Bar Diagram is most suitable.
Reason: We need to compare multiple variables (Production, Consumption, Exports) across two distinct time periods (2000 and 2001). Grouping these bars side-by-side allows for easy comparison.
(iii) Diagrammatic Presentation:
(Imagine a graph with X-axis = Year, Y-axis = Tonnes)
• Group 2000: Bar 1 (Prod: 3.78L), Bar 2 (Cons: 1.54L), Bar 3 (Exp: 0).
• Group 2001: Bar 1 (Prod: 3.87L), Bar 2 (Cons: 2.83L), Bar 3 (Exp: 0.41L).
| Year (Dec 1st Fortnight) | Total Production (Tonnes) | Off-take (Tonnes) | |
|---|---|---|---|
| Internal Consumption | Exports | ||
| 2000 | 3,78,000 | 1,54,000 | Nil |
| 2001 | 3,87,000 | 2,83,000 | 41,000 |
(ii) Diagram Choice:
A Multiple Bar Diagram is most suitable.
Reason: We need to compare multiple variables (Production, Consumption, Exports) across two distinct time periods (2000 and 2001). Grouping these bars side-by-side allows for easy comparison.
(iii) Diagrammatic Presentation:
(Imagine a graph with X-axis = Year, Y-axis = Tonnes)
• Group 2000: Bar 1 (Prod: 3.78L), Bar 2 (Cons: 1.54L), Bar 3 (Exp: 0).
• Group 2001: Bar 1 (Prod: 3.87L), Bar 2 (Cons: 2.83L), Bar 3 (Exp: 0.41L).
15. Represent the GDP sectoral growth rates as multiple time series graphs.
To represent this data:
(Use different styles/colors for lines: e.g., Solid for Agri, Dashed for Industry, Dotted for Services).
- X-axis: Years (1994-95 to 1999-2000).
- Y-axis: Growth Rate (%). Scale should span from -2.0 to 12.0.
- Plotting Lines:
- Line 1 (Agriculture): Starts at 5.0, drops to -0.9, spikes to 9.6, drops to -1.9, up to 7.2, down to 0.8. (Highly volatile).
- Line 2 (Industry): 9.2 → 11.8 → 6.0 → 5.9 → 4.0 → 6.9. (Fluctuating).
- Line 3 (Services): 7.0 → 10.3 → 7.1 → 9.0 → 8.3 → 8.2. (Relatively stable).
(Use different styles/colors for lines: e.g., Solid for Agri, Dashed for Industry, Dotted for Services).