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प्रश्न
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.
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उत्तर
Given that the times (in seconds) taken to solve a problem by each of 25 pupils are 16, 20, 26, 27, 28, 30, 33, 37, 38, 40, 42, 43, 46, 46, 46, 48, 49, 50, 53, 58, 59, 60, 64, 52 and 20. The minimum and maximum time values are 16 and 64 respectively.
(a) At first construct the following frequency distribution for the given data. Since, the lowest value is 16; we start with the class-interval 15-25, as the class size must be 10.
| Class - Intervals | Tally | Frequency |
| 15-25 | lll | 3 |
| 25-35 | lllll | 5 |
| 35-45 | lllll | 5 |
| 45-55 | llllllll | 8 |
| 55-65 | llll | 4 |
(b) 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 above data is a continuous grouped frequency distribution with equal class-intervals, which is 10. Construct rectangles with class-intervals as bases and respective frequencies as heights.
The histogram of the data in part (a) is as follows:
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संबंधित प्रश्न
The runs scored by two teams A and B on the first 60 balls in a cricket match are given below:
| Number of balls | Team A | Team B |
| 1 - 6 | 2 | 5 |
| 7 - 12 | 1 | 6 |
| 13 - 18 | 8 | 2 |
| 19 - 24 | 9 | 10 |
| 25 - 30 | 4 | 5 |
| 31 - 36 | 5 | 6 |
| 37 - 42 | 6 | 3 |
| 43 - 48 | 10 | 4 |
| 49 - 54 | 6 | 8 |
| 55 - 60 | 2 | 10 |
Represent the data of both the teams on the same graph by frequency polygons.
[Hint: First make the class intervals continuous.]
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(i) What is the information given by the bar graph?
(ii) State each of the following whether true or false.
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Read the bar graph given in Fig. 23.21 and answer the following questions:
(i) What is the information given by the bar graph?
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Explain the reading and interpretation of bar graphs.
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| Number of T.V. Sets | 300 | 400 | 150 | 250 | 100 | 350 | 200 |
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| Mode | Bus | Car | Bicycle | Auto | On foot |
| No. of students | 142 | 98 | 50 | 34 | 16 |
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In the following figure, there is a histogram depicting daily wages of workers in a factory. Construct the frequency distribution table.
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 |
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 |
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