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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
100 surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet in the surnames was found as follows:
| Number of letters | Number of surnames |
| 1 - 4 | 6 |
| 4 - 6 | 30 |
| 6 - 8 | 44 |
| 8 - 12 | 16 |
| 12 - 20 | 4 |
- Draw a histogram to depict the given information.
- Write the class interval in which the maximum number of surnames lie.
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?
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 population of Delhi State in different census years is as given below:
| Census year | 1961 | 1971 | 1981 | 1991 | 2001 |
| Population in Lakhs | 30 | 55 | 70 | 110 | 150 |
The following data gives the amount of manure (in thousand tonnes) manufactured by a company during some years:
| Year | 1992 | 1993 | 1994 | 1995 | 1996 | 1997 |
| Manure (in thousand tonnes) |
15 | 35 | 45 | 30 | 40 | 20 |
(i) Represent the above data with the help of a bar graph.
(ii) Indicate with the help of the bar graph the year in which the amount of manufactured by the company was maximum.
(iii) Choose the correct alternative:
The consecutive years during which there was maximum decrease in manure production are:
(a) 1994 and 1995
(b) 1992 and 1993
(c) 1996 and 1997
(d) 1995 and 1996
The following table gives the distribution of IQ's (intelligence quotients) of 60 pupils of class V in a school:
| IQ's: | 125.5 to 13.25 |
118.5 to 125.5 |
111.5 to 118.5 |
104.5 to 111.5 |
97.5 to 104.5 |
90.5 to 97.5 |
83.5 to 90.5 |
76.5 to 83.5 |
69.5 to 76.5 |
62.5 to 69.5 |
| No. of pupils: |
1 | 3 | 4 | 6 | 10 | 12 | 15 | 5 | 3 | 1 |
Draw a frequency polygon for the above data.
In a histogram the area of each rectangle is proportional to
The percentage of marks obtained, in different subjects by Ashok Sharma (in an examination) is given below. Draw a bar graph to represent it.
| English | Hindi | Maths | Science | Social Studies |
| 85 | 60 | 35 | 50 | 70 |
Draw a histogram to represent the following grouped frequency distribution:
| Ages (in years) | Number of teachers |
| 20 – 24 | 10 |
| 25 – 29 | 28 |
| 30 – 34 | 32 |
| 35 – 39 | 48 |
| 40 – 44 | 50 |
| 45 – 49 | 35 |
| 50 – 54 | 12 |
The lengths of 62 leaves of a plant are measured in millimetres and the data is represented in the following table:
| Length (in mm) | Number of leaves |
| 118 – 126 | 8 |
| 127 – 135 | 10 |
| 136 – 144 | 12 |
| 145 – 153 | 17 |
| 154 – 162 | 7 |
| 163 – 171 | 5 |
| 172 – 180 | 3 |
Draw a histogram to represent the data above.
