Central Tendency & DispersionMTP Mar 21Question 2893 of 473
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If sum of squares of the values = 3390, N = 30 and standard deviation = 7, find out the mean.

Options

A113
B210
C8
DNone of these
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Correct Answer

✅ Option c — 8

All Options:

  • A113
  • B210
  • C8
  • DNone of these

Detailed Solution & Explanation

**Step 1: Recall the relationship between variance, mean, and sum of squares.** σ2=∑xi2N−xˉ2\sigma^2 = \frac{\sum x_i^2}{N} - \bar{x}^2 Given: ∑xi2=3390\displaystyle \sum x_i^2 = 3390, N=30\displaystyle N = 30, σ=7⇒σ2=49\displaystyle \sigma = 7 \Rightarrow \sigma^2 = 49. **Step 2: Substitute and solve for xˉ\displaystyle \bar{x}.** 49=339030−xˉ249 = \frac{3390}{30} - \bar{x}^2 49=113−xˉ249 = 113 - \bar{x}^2 xˉ2=113−49=64\bar{x}^2 = 113 - 49 = 64 xˉ=64=8\bar{x} = \sqrt{64} = 8 **Note:** The computed mean is **8** (Option C), not 'None of these'. But given the `correct_option` is D, and Option C (8) is indeed the calculated answer, the correct answer by computation is **8**. Hence, **Option C** is the correct answer.

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