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प्रश्न
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 |
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उत्तर
The frequency polygon is shown in the following figure
Steps:
(i) Drawing a histogram for the given data.
(ii) Marking the mid-point at the top of each rectangle of the histogram drawn.
(iii) Also, marking mid-point of the immediately lower class-interval and mid-point of the immediately higher class-interval.
(iv) Joining the consecutive mid-points marked by straight lines to obtain the required frequency polygon.
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संबंधित प्रश्न
The length of 40 leaves of a plant are measured correct to one millimetre, and the obtained data is represented in the following table:-
| Length (in mm) | Number of leaves |
| 118 - 126 | 3 |
| 127 - 135 | 5 |
| 136 - 144 | 9 |
| 145 - 153 | 12 |
| 154 - 162 | 5 |
| 163 - 171 | 4 |
| 172 - 180 | 2 |
- Draw a histogram to represent the given data. [Hint: First make the class intervals continuous]
- Is there any other suitable graphical representation for the same data?
- Is it correct to conclude that the maximum number of leaves are 153 mm long? Why?
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.
Read the following bar graph (Fig. 23.12) and answer the following questions:
(i) What is the information given by the bar graph?
(ii) State each of the following whether true or false.
a. The number of government companies in 1957 is that of 1982 is 1 :9.
b. The number of government companies have decreased over the year 1957 to 1983.
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 production of oil (in lakh tonnes) in some of the refineries in India during 1982 was given below:
| Refinery: | Barauni | Koyali | Mathura | Mumbai | Florida |
| Production of oil (in lakh tonnes) |
30 | 70 | 40 | 45 | 25 |
Construct a bar graph to represent the above data so that the bars are drawn horizontally.
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.
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?
Is it correct to say that in a histogram, the area of each rectangle is proportional to the class size of the corresponding class interval? If not, correct the statement.
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.
