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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
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Solution

To draw a histogram for the given data, we need to follow these steps:

  1. 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.

  2. 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.

  3. 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
  4. 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
  5. 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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