The frequency distribution of the marks obtained by students in a Science examination is given below :<br><br><table> <thead><tr><th>Marks</th><th>5–15</th><th>15–25</th><th>25–35</th><th>35–45</th></tr></thead> <tbody> <tr><td>Number of<br>students</td><td>20</td><td>30</td><td>30</td><td>20</td></tr> </tbody> </table><br><br>What is the arithmetic mean?
- A. 20
- B. 25 ✓
- C. 30
- D. 35
Correct Answer: B. 25
Explanation
The midpoints (x_i) for the classes are 10, 20, 30, 40. The corresponding frequencies (f_i) are 20, 30, 30, 20. The arithmetic mean is \frac{\sum f_i x_i}{\sum f_i} = \frac{20(10) + 30(20) + 30(30) + 20(40)}{100} = \frac{200 + 600 + 900 + 800}{100} = \frac{2500}{100} = 25.
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