Marks scored by 104 students of a college in the mid-term exam given below. Draw histogram. Marks No. of students 0-24 12 24-40 16 40-48 24 48-68 40 68-80 12
Question
Marks scored by 104 students of a college in the mid-term exam given below. Draw histogram. Marks No. of students 0-24 12 24-40 16 40-48 24 48-68 40 68-80 12
Solution
To draw a histogram for the given data, we need to follow these steps:
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Determine the range of the data: The range is the difference between the maximum and minimum values. In this case, the minimum value is 0 and the maximum value is 80, so the range is 80 - 0 = 80.
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Determine the number of intervals: The number of intervals can be determined based on the range and the desired width of each interval. In this case, we can choose a width of 10. So, the number of intervals is 80 / 10 = 8.
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Create the intervals: Divide the range into the chosen number of intervals. In this case, the intervals would be:
- 0-10
- 10-20
- 20-30
- 30-40
- 40-50
- 50-60
- 60-70
- 70-80
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Count the frequency: Count the number of data points that fall into each interval. In this case, we have the following frequencies:
- 0-10: 0 students
- 10-20: 0 students
- 20-30: 0 students
- 30-40: 16 students
- 40-50: 24 students
- 50-60: 0 students
- 60-70: 12 students
- 70-80: 12 students
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Draw the histogram: On a graph paper, draw a horizontal axis representing the intervals and a vertical axis representing the frequency. For each interval, draw a rectangle with a height equal to the frequency. The width of the rectangle can be proportional to the width of the interval.
In this case, the histogram would look like this:
Frequency
24 | ______
20 | | |
16 | | |
12 | | |
8 | | |
4 | | |
0 |_____________________
0-10 10-20 20-30 ...
This histogram represents the distribution of marks scored by the students in the mid-term exam.
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