What is the mode of the distribution?

A frequency distribution is as follows:<br> <table> <thead> <tr><th>Marks</th><th>18–26</th><th>27–35</th><th>36–44</th><th>45–53</th><th>54–62</th><th>63–71</th><th>72–80</th></tr> </thead> <tbody> <tr><td>Number of students</td><td>5</td><td>7</td><td>10</td><td>15</td><td>8</td><td>3</td><td>2</td></tr> </tbody> </table>

  1. A. 47.25
  2. B. 47.75
  3. C. 48.25 ✓
  4. D. 48.75

Correct Answer: C. 48.25

Explanation

The modal class is the continuous interval 44.5-53.5 with maximum frequency f_m = 15, previous f_1 = 10, next f_2 = 8, and class width h = 9. Mode = L + \frac{f_m - f_1}{2f_m - f_1 - f_2} \times h = 44.5 + \frac{15 - 10}{30 - 10 - 8} \times 9 = 44.5 + \frac{5}{12} \times 9 = 44.5 + 3.75 = 48.25.

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