Measures of Central Tendency and DispersionMCQMTP 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

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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.

About This Chapter: Measures of Central Tendency and Dispersion

Paper

Paper 3: Quantitative Aptitude

Weightage

12-15 Marks

Key Topics

Mean, Median, Mode, Range, Mean Deviation, Standard Deviation

The core foundation of Statistics. This chapter covers Mean (Arithmetic, Geometric, Harmonic), Median, Mode, and their properties. It also explores measures of spread like Range, Mean Deviation, Standard Deviation, and Quartile Deviation.

View Official ICAI Syllabus

Exam Strategy Tip

Do not just memorize formulas; ICAI loves asking about the mathematical properties (e.g., 'sum of deviations from the AM is always zero'). You can usually eliminate 2 options just by knowing the properties.

Key Concepts to Understand

Standard Deviation

A measure of the dispersion or spread of values in a data set around the mean. It is the square root of Variance. A lower standard deviation indicates data points are clustered close to the mean; a higher value indicates greater spread.

Related Comparison Tables

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