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प्रश्न
The following is the distribution of total household expenditure (in Rs.) of manual worker in a city:
| Expenditure (in Rs): |
100-150 | 150-200 | 200-250 | 250-300 | 300-350 | 350-400 | 400-450 | 450-500 |
| No. of manual workers: | 25 | 40 | 33 | 28 | 30 | 22 | 16 | 8 |
Draw a histogram and a frequency polygon representing the above data.
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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 5 workers.
The heights of the different rectangles are as follows:
1. The height of the rectangle corresponding to the class-interval 100-150 is `25/5=5` big divisions.
2. The height of the rectangle corresponding to the class-interval 150-200 is `40/5=8` big divisions.
3. The height of the rectangle corresponding to the class-interval 200-250 is ` 33/5 = 6.6` big divisions.
4. The height of the rectangle corresponding to the class-interval 250-300 is `28/5 = 5.6 ` big divisions.
5. The height of the rectangle corresponding to the class-interval 300-350 is ` 30/5 =6 ` big divisions.
6. The height of the rectangle corresponding to the class-interval 350-400 is ` 22/5 = 4.4` big divisions.
7. The height of the rectangle corresponding to the class-interval 400-450 is ` 16/5 = 3.2` big division.
8. The height of the rectangle corresponding to the class-interval 450-500 is ` 8/5 = 1.6` big divisions.
The histogram of the given data is as follows:
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संबंधित प्रश्न
The following data on the number of girls (to the nearest ten) per thousand boys in different sections of Indian society is given below.
| Section | Number of girls per thousand boys |
| Scheduled Caste (SC) | 940 |
| Scheduled Tribe (ST) | 970 |
| Non SC/ST | 920 |
| Backward districts | 950 |
| Non-backward districts | 920 |
| Rural | 930 |
| Urban | 910 |
- Represent the information above by a bar graph.
- In the classroom discuss what conclusions can be arrived at from the graph.
Read the bar graph given in Fig. 23.20 and answer the fol1owing questions:
(i) What information is given by the bar graph?
(ii) What was the expenditure on health and family planning in the year 1982-83?
(iii) In which year is the increase in expenditure maximum over the expenditure in previous year? What is the maximum increase?
The following table gives the route length (in thousand kilometres) of the Indian Railways in some of the years:
| Year | 1960-61 | 1970-71 | 1980-81 | 1990-91 | 2000-2001 |
| Route length (in thousand km) |
56 | 60 | 61 | 74 | 98 |
Represent the above data with the help of a bar graph.
The following data gives the production of foodgrains (in thousand tonnes) for some years:
| Year | 1995 | 1996 | 1997 | 1998 | 1999 | 2000 |
| Production (in thousand tonnes |
120 | 150 | 140 | 180 | 170 | 190 |
Represent the above with the help of a bar graph.
The following tables gives the quantity of goods (in crore tonnes)
| Year | 1950-51 | 1960-61 | 1965-66 | 1970-71 | 1980-81 | 1982-83 |
| Quantity of Goods (in crore tonnes) |
9 | 16 | 20 | 20 | 22 | 26 |
Explain through the bar graph if the quantity of goods carried by the Indian Railways in 1965-66 is more than double the quantity of goods carried in the year 1950-51.
The expenditure (in 10 crores of rupees) on health by the Government of India during the various five year plans is shown below:
| Plans: | I | II | III | IV | V | VI |
| Expenditure on health (in 10 crores of rupees) |
7 | 14 | 23 | 34 | 76 | 182 |
Construct a bar graph to represent the above data.
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 |
In a histogram the class intervals or the group are taken along
Harmeet earns Rs.50 000 per month. He a budget for his salary as per the following table:
| Expenses | Accommodation | Food | Clothing | Travel | Miscellaneous | saving |
| Amount (Rs.) | 12000 | 9000 | 2500 | 7500 | 4000 | 15000 |
Draw a bar graph for the above data.
The expenditure of a family on different heads in a month is given below:
| Head | Food | Education | Clothing | House Rent | Others | Savings |
| Expenditure (in Rs) |
4000 | 2500 | 1000 | 3500 | 2500 | 1500 |
Draw a bar graph to represent the data above.
