What is the median 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>
- A. 44.9
- B. 45.5
- C. 45.9
- D. 46.3 ✓
Correct Answer: D. 46.3
Explanation
Convert to continuous classes: 17.5-26.5, 26.5-35.5, etc., with class size h=9. Total frequency N=50. Median class is 44.5-53.5 (since cumulative frequency crosses 25 here, cf=22 for previous class). Median = L + \frac{\frac{N}{2} - cf}{f} \times h = 44.5 + \frac{25 - 22}{15} \times 9 = 44.5 + 1.8 = 46.3.
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