Central Tendency & DispersionPYQ Dec 22Question 3138 of 473
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If the sum of square of the values equals to 3390, Number of observations are 30 and Standard deviation is 7, what is the mean value of the above observations?

Options

A14\displaystyle 14
B11\displaystyle 11
C8\displaystyle 8
D5\displaystyle 5
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Correct Answer

✅ Option c — 8\displaystyle 8

All Options:

  • A14\displaystyle 14
  • B11\displaystyle 11
  • C8\displaystyle 8
  • D5\displaystyle 5

Detailed Solution & Explanation

**Given:** ∑xi2=3390\displaystyle \sum x_i^2 = 3390, n=30\displaystyle n = 30, σ=7\displaystyle \sigma = 7 **Step 1: Use the variance formula.** σ2=∑xi2n−xˉ2\sigma^2 = \frac{\sum x_i^2}{n} - \bar{x}^2 72=339030−xˉ27^2 = \frac{3390}{30} - \bar{x}^2 49=113−xˉ249 = 113 - \bar{x}^2 **Step 2: Solve for xˉ2\displaystyle \bar{x}^2.** xˉ2=113−49=64\bar{x}^2 = 113 - 49 = 64 **Step 3: Solve for xˉ\displaystyle \bar{x}.** xˉ=64=8\bar{x} = \sqrt{64} = 8 Wait — the answer is 8, but the given `correct_option` is 'b' which is 11\displaystyle 11. Let me recheck: 339030=113\displaystyle \frac{3390}{30} = 113; 113−49=64\displaystyle 113 - 49 = 64; 64=8\displaystyle \sqrt{64} = 8. So the mean = **8**, which is Option C. Let me verify Option B (xˉ=11\displaystyle \bar{x} = 11): σ2=113−121=−8\displaystyle \sigma^2 = 113 - 121 = -8 — impossible (negative variance). Let me verify Option A (xˉ=14\displaystyle \bar{x} = 14): σ2=113−196=−83\displaystyle \sigma^2 = 113 - 196 = -83 — impossible. Let me verify Option D (xˉ=5\displaystyle \bar{x} = 5): σ2=113−25=88\displaystyle \sigma^2 = 113 - 25 = 88; σ=88≈9.38≠7\displaystyle \sigma = \sqrt{88} \approx 9.38 \neq 7. **The correct mathematical answer is xˉ=8\displaystyle \bar{x} = 8 (Option C).** Hence, **Option C** is the correct answer.

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