NCERT Solution for Class 11 Commerce Statistics for Economics Chapter 4 - Presentation of Data
NCERT Solution for Class 11 Commerce Statistics for Economics Chapter 4 - Presentation of Data Page/Excercise 56
The correct answer is option (i).
A bar diagram is a one-dimensional diagram which represents categorical data. This is because only the length of the bars is used for comparative analysis. This is the most commonly used diagram which presents the data in the form of bars or rectangles.
The correct answer is option (ii).
Graphically, the histogram provides the value of the mode of the frequency distribution. The rectangle with the greatest height will be the modal class. If we draw a line joining the top right of the rectangle of the modal class with the top right point of the rectangle of the class preceding the modal class and the other line joining the top left point of the rectangle of the modal class with the top left point of the rectangle of the class succeeding the modal class, then the line drawn from the point of intersection of the two diagonal lines will be perpendicular to the X-axis. Thus, the point at which the perpendicular touches the X-axis gives the required modal value.
The correct answer is option (iii).
Graphically, the ogive curve is constructed by plotting the cumulative frequency data. This curve represents the frequencies corresponding to the lower limits or the upper limits in the distribution. This curve can be constructed by the less than method, i.e. frequencies cumulated corresponding to the upper limits of the class in the distribution or more than method, i.e. frequencies cumulated corresponding to the lower limits of the class in the distribution. Thus, the point at which the two ogive curves intersect each other is the median.
The correct answer is option (i).
An arithmetic line represents time which is plotted along the X-axis and the corresponding value of the variable along the Y-axis. This helps in understanding the trend and periodicity in long-term time series data.
- The statement is False. The bar diagram consists of a group of equal space and equal width rectangular bars for each class of data. Thus, the width of the bars have the same width in a bar diagram.
- The statement is False. Width of rectangles in a histogram is not necessarily equal because some type of data may vary in the width of the class interval, and therefore, the width of a rectangle varies accordingly. Generally, the width of a rectangle in a histogram is as significant as its height.
- The statement is True. This histogram can never be drawn for discrete data because the lower class boundary of a class interval fuses with the upper class boundary of the previous interval. Rectangles are adjacent to each other and there is no open space between two consecutive rectangles. Thus, a histogram can only be formed with continuous classification of data.
- The statement is False. A histogram and a column/bar diagram may look similar, but there are certain differences between them such as
- A histogram is a two-dimensional diagram, whereas a column or bar diagram is a one-dimensional diagram.
- A histogram has no space between two rectangles, but a bar diagram has equal space between two rectangles.
- A histogram is drawn for a continuous variable, whereas a bar diagram is drawn for both discrete and continuous variables.
Thus, a histogram and column diagram are two methods of presenting data.
- The statement is True. Graphically, the histogram provides the value of mode of the frequency distribution. The rectangle with the greatest height will be the modal class. If we draw a line joining the top right of the rectangle of the modal class with the top right point of the rectangle of the class preceding the modal class and the other line joining the top left point of the rectangle of the modal class with the top left point of the rectangle of the class succeeding the modal class, then the line drawn from the point of intersection of the two diagonal lines will be perpendicular to the X-axis. Thus, the point at which the perpendicular touches the X-axis gives the required modal value.
- The statement is False. Graphically, an ogive curve is constructed by plotting the cumulative frequency data. This curve represents the frequencies corresponding to the lower limits or upper limits in the distribution. This curve can be constructed by the less than method, i.e. frequencies cumulated corresponding to the upper limits of the class in the distribution or more than method, i.e. frequencies cumulated corresponding to the lower limits of the class in the distribution. Thus, the point at which the two ogive curves intersect each other is the median of frequency distribution.
NCERT Solution for Class 11 Commerce Statistics for Economics Chapter 4 - Presentation of Data Page/Excercise 57
- Monthly rainfall in a year: The monthly rainfall in a year can be diagrammatically presented in a bar diagram. In this diagram, data can be presented in the form of bars or rectangles. These bars can be compared by their relative height, and so, the highest monthly rainfall in a year is comprehended easily.
- Composition of the population of Delhi by religion: Composition of the population of Delhi by religion can be diagrammatically presented in a simple bar diagram. This diagram is based on a single set of data of numerical data. Here, the X-axis represents different religion and the Y-axis represents the composition of the population of Delhi. According to the composition of the population of Delhi of different religions, the corresponding bars are made of the respective heights to construct a simple bar diagram. This helps compare and analyse the composition of the population of Delhi by religion.
- Components of cost in a factory: The components of cost in a factory can be diagrammatically presented in a pie diagram. Values of each component of costs in a factory are first expressed as percentage of the total value of all the components of cost. Different parts of a circle represent the value of different components of cost in a factory.
Given that
Share of urban non-workers in India = 7 + 12 + 19 = 38 crore
Share of rural non-workers in India = 18 + 25 + 43 = 86 crore
Rural and Urban Non-workers in India
Share of rural non-workers in India (in crore) |
Share of urban non-workers in India (in crore) |
Total non-workers in India |
86 |
38 |
134 |
Source: Census of India, 2001
Based on the given information, we can observe that the share of rural non-workers is more than the share of urban non-workers in India. Greater share of rural non-workers indicates a lower level of urbanisation in India.
Note: Please note the correction in the given question; instead of example 4.2 refer to Table 4.5 in the book.
A histogram of equal class intervals has rectangles of equal width. If the data of class intervals are unequal, then the width of rectangles will be different.
Procedure to draw a histogram of unequal class intervals
- Frequencies of unequal class intervals are adjusted before presenting the data in the form of graphs.
- Formula applied to adjust the unequal class intervals is
- Finally, the original frequency is divided by the adjustment factor to arrive at the adjusted frequency.
- Given information presented in a tabular form:
Sugar Production in India |
|||
Period |
Total Production (in tonne) |
Internal Consumption (in tonne) |
Export of Sugar (in tonne) |
1st Fortnight, December 2000 |
3,78,000 |
1,54,000 |
0 |
1st Fortnight, December 2001 |
3,87,000 |
2,83,000 |
41,000 |
Source: Indian Sugar Mills Association Report
- Sugar production in India can be presented diagrammatically in a multiple bar diagram. This method of representing data is useful to compare two or more sets of data such as internal consumption and export of sugar in the first quarters of December 2000 and 2001.
- Diagrammatic representation of the data provided in the tabular form: