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Question
A Mathematics aptitude test of 50 students was recorded as follows:
| Marks | 50 - 60 | 60 - 70 | 70 - 80 | 80 - 90 | 90 – 100 |
| No. of Students | 4 | 8 | 14 | 19 | 5 |
Draw a histogram from the above data using a graph paper and locate the mode.
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Solution
The histogram for the given data can be drawn by taking the marks on the x-axis and the number of students on the y-axis.
To locate the mode from the histogram, we proceed as follows:
1) Find the modal class. Rectangle ABCD is the largest rectangle. It represents the modal class, that is, the mode lies in this rectangle. The modal class is 80 – 90.
2) Draw two lines diagonally from the vertices C and D to the upper corners of the two adjacent rectangles. Let these rectangles intersect at point H.
3) The x-value of the point H is the mode. Thus, mode of the given data is approximately 83.
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RELATED QUESTIONS
The histogram below represents the scores obtained by 25 students in a mathematics mental test. Use the data to:
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- To calculate mean.
- To determine the Modal class.
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| Frequency | 15 | 23 | 30 | 20 | 16 |
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| 5800−5900 | 3 |
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| 6100−6200 | 3 |
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| Pocket expenses (in ₹) |
Number of students (frequency) |
| 0 - 5 | 10 |
| 5 - 10 | 14 |
| 10 - 15 | 28 |
| 15 - 20 | 42 |
| 20 - 25 | 50 |
| 25 - 30 | 30 |
| 30 - 35 | 14 |
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Draw a histogram representing the above distribution and estimate the mode from the graph.
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- How many students have height more than or equal to 135 cm but less than 150 cm?
- Which class interval has the least number of students?
- What is the class size?
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Draw a histogram to represent the frequency distribution in question 91.
