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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
Given below are the seats won by different political parties in the polling outcome of a state assembly elections:-
| Political Party | A | B | C | D | E | F |
| Seats Won | 75 | 55 | 37 | 29 | 10 | 37 |
- Draw a bar graph to represent the polling results.
- Which political party won the maximum number of seats?
Given below (Fig. below) is the bar graph indicating the marks obtained out of 50 in mathematics paper by 100 students. Read the bar graph and answer the following questions:
(i) It is decided to distribute work books on mathematics to the students obtaining less than 20 marks, giving one workbook to each of such students. If a work book
costs Rs 5, what sum is required to buy the work books?
(ii) Every student belonging to the highest mark group is entitled to get a prize of Rs. 10. How much amount of money is required for distributing the prize money?
(iii) Every student belonging to the lowest mark—group has to solve 5 problems per day. How many problems, in all, will be solved by the students of this group per day?
(iv) State whether true or false.
a. 17% students have obtained marks ranging from 40 to 49.
b. 59 students have obtained marks ranging from 10 to 29.
(v) What is the number of students getting less than 20 marks?
(vi) What is the number of students getting more than 29 marks?
(vii) What is the number of students getting marks between 9 and 40?
(viii) What is the number of students belonging to the highest mark group?
(ix) What is the number of students obtaining more than 19 marks?
The following table shows the interest paid by a company (in lakhs):
| Year | 1995-96 | 1996-97 | 1997-98 | 1998-99 | 1999-2000 |
| Interest (in lakhs of rupees | 20 | 25 | 15 | 18 | 30 |
Draw the bar graph to represent the above information.
The time taken, in seconds, to solve a problem by each of 25 pupils is as follows:
16, 20, 26, 27, 28, 30, 33, 37, 38, 40, 42, 43, 46, 46, 46, 48, 49, 50, 53, 58, 59, 60, 64, 52, 20
(a) Construct a frequency distribution for these data, using a class interval of 10 seconds.
(b) Draw a histogram to represent the frequency distribution.
A histogram is a pictorial representation of the grouped data in which class intervals and frequency are respectively taken along
Construct a frequency polygon for the following distribution:
| Class-intervals | 0-4 | 4 - 8 | 8 - 12 | 12 - 16 | 16 - 20 | 20 - 24 |
| Frequency | 4 | 7 | 10 | 15 | 11 | 6 |
Mr. Kapoor compares the prices (in Rs.) of different items at two different shops A and B. Examine the following table carefully and represent the data by a double bar graph.
| Items | Price (in ₹) at the shop A | Price (in ₹) at the shop B |
|
Tea-set |
900 | 950 |
|
Mixie |
700 | 800 |
|
Coffee-maker |
600 | 700 |
|
Dinner set |
600 | 500 |
The frequency distribution has been represented graphically as follows:
| Marks | 0 – 20 | 20 – 40 | 40 – 60 | 60 – 100 |
| Number of Students | 10 | 15 | 20 | 25 |
Do you think this representation is correct? Why?
Draw a histogram of the following distribution:
| Heights (in cm) | Number of students |
| 150 – 153 | 7 |
| 153 – 156 | 8 |
| 156 – 159 | 14 |
| 159 – 162 | 10 |
| 162 – 165 | 6 |
| 165 – 168 | 5 |
The marks obtained (out of 100) by a class of 80 students are given below:
| Marks | Number of students |
| 10 – 20 | 6 |
| 20 – 30 | 17 |
| 30 – 50 | 15 |
| 50 – 70 | 16 |
| 70 – 100 | 26 |
Construct a histogram to represent the data above.
