If average weekly wages earned by a worker is ₹ 3,520, then what is the value of k?
Consider the following for the next two (02) items that follow : A grouped frequency distribution is given below : <table> <thead><tr><th>Weekly wages in Rupees (₹)</th><th>Numbers of workers</th></tr></thead> <tbody> <tr><td>2050–2550</td><td>5</td></tr> <tr><td>2550–3050</td><td>10</td></tr> <tr><td>3050–3550</td><td>k</td></tr> <tr><td>3550–4050</td><td>8</td></tr> <tr><td>4050–4550</td><td>2</td></tr> <tr><td>4550–5050</td><td>10</td></tr> </tbody> </table>
- A. 10
- B. 12
- C. 15 ✓
- D. 20
Correct Answer: C. 15
Explanation
The class midpoints x_i are 2300, 2800, 3300, 3800, 4300, 4800. The sum of frequencies is 35+k, and \sum f_i x_i = 126500 + 3300k. The mean is \frac{126500 + 3300k}{35+k} = 3520, which solves to 126500 + 3300k = 123200 + 3520k \implies 220k = 3300 \implies k = 15.
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