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प्रश्न
Draw, in the same diagram, a histogram and a frequency polygon to represent the following data which shows the monthly cost of living index of a city in a period of 2 years:
| Cost of living index: |
440-460 | 460-480 | 480-500 | 500-520 | 520-540 | 540-560 | 560-580 | 580-600 |
| No. of months: | 2 | 4 | 3 | 5 | 3 | 2 | 1 | 4 |
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उत्तर
To represent the given data by a histogram, we first draw horizontal and vertical axes. Let us consider that the horizontal and vertical axes represent the class-limits and the frequencies of the class-intervals respectively.
The given data is a continuous grouped frequency distribution with equal class-intervals. Construct rectangles with class-intervals as bases and respective frequencies as heights. It should be noted that the scale for horizontal axis may not be same as the scale for vertical axis. To draw the frequency polygon of the given data using histogram, obtain the mid-points of the upper horizontal side of each rectangle and then join these mid-points of the adjacent rectangles of the histogram by line segments. Obtain the mid-points of two class-intervals of 0 frequencies, i.e. on the horizontal axis, one adjacent to the first, on its left and one adjacent to the last, on its right. These class-intervals are known as imagined class-intervals. Complete the polygon by joining the mid-points of first and last class-intervals to the mid-points of imagined class-intervals adjacent to them. Let us take one vertical division is equal to 1 month.
The heights of the different rectangles are as follows:
1. The height of the rectangle corresponding to the class-interval 440-460 is 2 big divisions.
2. The height of the rectangle corresponding to the class-interval 460-480 is 4 big divisions.
3. The height of the rectangle corresponding to the class-interval 480-500 is 3 big divisions.
4. The height of the rectangle corresponding to the class-interval 500-520 is 5 big divisions.
5. The height of the rectangle corresponding to the class-interval 520-540 is 3 big divisions.
6. The height of the rectangle corresponding to the class-interval 540-560 is 2 big divisions.
7. The height of the rectangle corresponding to the class-interval 560-580is 1 big division.
8. The height of the rectangle corresponding to the class-interval 580-600 is 4 big divisions.
The histogram and frequency polygon of the given data is as follows:
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संबंधित प्रश्न
The following table gives the distribution of students of two sections according to the mark obtained by them:-
| Section A | Section B | ||
| Marks | Frequency | Marks | Frequency |
| 0 - 10 | 3 | 0 - 10 | 5 |
| 10 - 20 | 9 | 10 - 20 | 19 |
| 20 - 30 | 17 | 20 - 30 | 15 |
| 30 - 40 | 12 | 30 - 40 | 10 |
| 40 - 50 | 9 | 40 - 50 | 1 |
Represent the marks of the students of both the sections on the same graph by two frequency polygons. From the two polygons compare the performance of the two sections.
Read the bar graph shown in Fig. 23.10 and answer the following questions
(i) What is the information given by the bar graph?
(ii) What was the number of commercial banks in 1977?
(iii) What is the ratio of the number of commercial banks in 1969 to that in 1980?
(iv) State whether true or false:
The number of commercial banks in 1983 is less than double the number of commercial banks in 1969.
Read the bar graph given in Fig. 23.17 and answer the following questions:
(i) What information is given by the bar graph?
(ii) What was the crop-production of rice in 1970 - 71?
(iii) What is the difference between the maximum and minimum production of rice?
Read the bar graph given in Fig. below and answer the following questions:
(i) What information does it give?
(ii) In which part the expenditure on education is maximum in 1980?
(iii) In which part the expenditure has gone up from 1980 to 1990?
(iv) In which part the gap between 1980 and 1990 is maximum?
Read the bar graph given in Fig. 23.19 and answer the following questions:
(i) What information is given by the bar graph?
(ii) In which years the areas under the sugarcane crop were the maximum and the minimum?
(iii) State whether true or false:
The area under the sugarcane crop in the year 1982 - 83 is three times that of the year 1950 - 51
Read the bar graph given in Fig. 23.22 and answer the following questions:
(i) What information is given by the bar graph?
(ii) Which Doordarshan centre covers maximum area? Also tell the covered area.
(iii) What is the difference between the areas covered by the centres at delhi and Bombay?
(iv) Which Doordarshan centres are in U.P State? What are the areas covered by them?
The investment (in ten crores of rupees) of Life Insurance Corporation of India in different sectors are given below:
| Sectors | Investment (in ten crores of rupees) |
| Central Government Securities State Government Securities Securities guaranteed by the Government Private Sectors Socially oriented sectors (Plans) Socially oriented sectors (Non-Plan) |
45 11 23 18 46 11 |
Represent the above data with the help of bar graph.
The following tables show the mode of transport used by boys and girls for going to the same school.
| Bus | Bicycle | Walking | Other sources | |
|
Number of boys |
80 | 60 | 20 | 85 |
|
Number of girls |
90 | 75 | 35 | 60 |
Draw a double bar graph representing the above data.
The birth rate thousand of the following states over a certain period is given below:
| States | Punjab | Haryana | U.P. | Gujarat | Rajasthan | Jammu and Kashmir |
| Birth Rate (per thousand ) | 22.9 | 21.8 | 19.5 | 21.1 | 23.9 | 18.3 |
Draw a bar graph for the above data.
Following table gives the distribution of students of sections A and B of a class according to the marks obtained by them.
| Section A | Section B | ||
| Marks | Frequency | Marks | Frequency |
| 0 – 15 | 5 | 0 – 15 | 3 |
| 15 – 30 | 12 | 15 – 30 | 16 |
| 30 – 45 | 28 | 30 – 45 | 25 |
| 45 – 60 | 30 | 45 – 60 | 27 |
| 60 –75 | 35 | 60 – 75 | 40 |
| 75 – 90 | 13 | 75 – 90 | 10 |
Represent the marks of the students of both the sections on the same graph by two frequency polygons. What do you observe?
