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प्रश्न
Following table shows a frequency distribution for the speed of cars passing through at a particular spot on a high way:
| Class interval (km/h) | Frequency |
| 30 – 40 | 3 |
| 40 – 50 | 6 |
| 50 – 60 | 25 |
| 60 – 70 | 65 |
| 70 – 80 | 50 |
| 80 – 90 | 28 |
| 90 – 100 | 14 |
Draw a histogram and frequency polygon representing the data above.
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उत्तर
Clearly, the given frequency distribution is in exclusive form.
Along the horizontal axis, we represent the class intervals on some suitable scale. The corresponding frequencies are represented along the vertical axis on a suitable scale.
We construct rectangles with class intervals as the bases and the respective frequencies as the heights.
Let us draw a histogram for this data and mark the mid-points of the top of the rectangles as B, C, D, E, F, G and H, respectively. Here, the first class is 30 – 40 and the last class is 90 – 100.
Also, consider the imagined classes 20 – 30 and 100 – 110 each with frequency 0. The class marks of these classes are 25 and 105 at the points A and I, respectively.
Join all these points by dotted line.
Then, the curve ABCDEFGHI is the required frequency polygon.
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संबंधित प्रश्न
The following bar graph (Fig. 23. 1 4) represents the heights (in cm) of 50 students of Class XI of a particular school. Study the graph and answer the following questions:
(i) What percentage of the total number of students have their heights more than 149cm?
(ii) How many students in the class are in the range of maximum height of the class?
(iii) The school wants to provide a particular type of tonic to each student below the height
of 150 cm to improve his height. If the cost of the tonic for each student comes out to be Rs. 55, how much amount of money is required?
(iv) How many students are in the range of shortest height of the class?
(v) State whether true or false:
a. There are 9 students in the class whose heights are in the range of 155 - 159 cm.
b. Maximum height (in cm) of a student in the class is 17.
c. There are 29 students in the class whose heights are in the range of 145- 154 cm.
d. Minimum height (in cm) of a student is the class is in the range of 140 – 144 cms.
e. The number of students in the class having their heights less than 150 cm is 12.
f. There are 14 students each of whom has height more than 154. cm.
Explain the reading and interpretation of bar graphs.
Read the following bar graph and answer the following questions:
(i) What information is given by the bar graph?
(ii) In which year the export is minimum?
(iii)In which year the import is maximum?
(iv)In which year the difference of the values of export and import is maximum?
The following data shows the average age of men in various countries in a certain year:
| Country | India | Nepal | China | Pakistan | U.K | U.S.A |
| Average age (in years) |
55 | 52 | 60 | 50 | 70 | 75 |
Represent the above information by a bar graph.
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.
In a histogram, each class rectangle is constructed with base as
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 number of students (boys and girls) of class IX participating in different activities during their annual day function is given below:
| Activities | Dance | Speech | Singing | Quiz | Drama | Anchoring |
| Boys | 12 | 5 | 4 | 4 | 10 | 2 |
| Girls | 10 | 8 | 6 | 3 | 9 | 1 |
Draw a double bar graph for the above data.
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.
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?
