Measures of Central Tendency and DispersionMCQPYQ Nov 18Question 3118 of 473
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If the standard deviation for the marks obtained by a student in monthly test is 36\displaystyle 36, then variance is

Options

A6\displaystyle 6
B36\displaystyle 36
C1296\displaystyle 1296
DNone of these
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Correct Answer

✅ Option c — 1296\displaystyle 1296

All Options:

  • A6\displaystyle 6
  • B36\displaystyle 36
  • C1296\displaystyle 1296
  • DNone of these

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Detailed Solution & Explanation

By definition, the variance of a dataset is the square of its standard deviation. Mathematically: Variance=σ2\text{Variance} = \sigma^2 We are given the standard deviation is σ=36\displaystyle \sigma = 36. Therefore, the variance is: Variance=362=1296\text{Variance} = 36^2 = 1296 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.

Variance

A measure of dispersion equal to the average of the squared deviations of each data point from the mean. Formula: σ² = Σ(xᵢ − x̄)² / n. Standard Deviation = √Variance.

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