Multiple choice

The following data summarises the result of a certain examination Class-marks 0-5 5-15 15-25 25-35 35-45 45-55 55-65 65-75 No. of students 0 2 16 36 27 11 8 0 Draw the histogram of the above distribution and f ind the approximate measure of the central tendency(Mode) using histogram

  1. Mode $\approx$ 35
  2. Mode $\approx$ 32
  3. Mode $\approx$ 27
  4. Mode $\approx$ 20
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B Correct answer
Explanation

The modal class is 25-35 because it has the highest frequency, 36. Using the grouped-data mode formula gives 25 + (36 - 16)/(2 x 36 - 16 - 27) x 10, which is approximately 31.9. Thus the approximate mode is 32.

AI explanation

The modal class corresponds to the highest bar on the histogram, which is the class interval 25 to 35 with 36 students. To approximate the mode graphically, one draws straight lines from the top corners of the modal class bar to the top corners of the adjacent bars. The x-coordinate of the point where these two lines intersect falls inside the modal class, providing a mode of approximately 32.

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