Central Tendency & DispersionMTP Nov 18Question 2879 of 473
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The mean salary for a group of for a group of 50 male workers is Rs.4800 per month and that for a group of 50 female workers is Rs. 5600. the combined mean salary is

Options

A5100
B5200
C5300
D5400
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Correct Answer

✅ Option b — 5200

All Options:

  • A5100
  • B5200
  • C5300
  • D5400

Detailed Solution & Explanation

**Step 1: Identify the given data.** nm=50\displaystyle n_m = 50, xˉm=4800\displaystyle \bar{x}_m = 4800 (males); nf=50\displaystyle n_f = 50, xˉf=5600\displaystyle \bar{x}_f = 5600 (females). **Step 2: Apply combined mean formula.** xˉcombined=nmxˉm+nfxˉfnm+nf=50×4800+50×560050+50\bar{x}_{combined} = \frac{n_m \bar{x}_m + n_f \bar{x}_f}{n_m + n_f} = \frac{50 \times 4800 + 50 \times 5600}{50 + 50} =240000+280000100=520000100=5200= \frac{240000 + 280000}{100} = \frac{520000}{100} = 5200 **Note:** The computed answer is **5200** (Option B), not 5100 (Option A). Since both groups have equal size (50 each), the combined mean is simply 4800+56002=5200\displaystyle \frac{4800+5600}{2} = 5200. Hence, **Option B** is the correct answer.

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