Central Tendency & DispersionPYQ Nov 18Question 2859 of 473
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If total frequencies of three series are 50, 60 and 90 and their means are 12, 15 and 20 respectively, then the mean of their composite series is

Options

A16\displaystyle 16
B15.5\displaystyle 15.5
C16.5\displaystyle 16.5
D14.5\displaystyle 14.5
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Correct Answer

✅ Option c — 16.5\displaystyle 16.5

All Options:

  • A16\displaystyle 16
  • B15.5\displaystyle 15.5
  • C16.5\displaystyle 16.5
  • D14.5\displaystyle 14.5

Detailed Solution & Explanation

**Step 1: State the given data.** | Series | Frequency (ni\displaystyle n_i) | Mean (xˉi\displaystyle \bar{x}_i) | Total (nixˉi\displaystyle n_i \bar{x}_i) | |--------|-------------------|---------------------|-------------------------| | 1 | 50 | 12 | 600 | | 2 | 60 | 15 | 900 | | 3 | 90 | 20 | 1800 | **Step 2: Compute combined mean using the formula.** xˉcombined=n1xˉ1+n2xˉ2+n3xˉ3n1+n2+n3\bar{x}_{combined} = \frac{n_1\bar{x}_1 + n_2\bar{x}_2 + n_3\bar{x}_3}{n_1 + n_2 + n_3} =600+900+180050+60+90=3300200=16.5= \frac{600 + 900 + 1800}{50 + 60 + 90} = \frac{3300}{200} = 16.5 **Conclusion:** The combined mean is **16.5**. Hence, **Option C** is the correct answer.

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