The variance of the data 3, 4, 5, 8 is

Option b: 3.5. Solution: Given data: 3, 4, 5, 8; n = 4 Step 1: Calculate Mean. x = 3+4+5+8/4 = 20/4 = 5 Step 2: Calculate squared deviations. |c|c|c| xi & (xi - 5) & (xi - 5)2 3 & -2 & 4 4 & -1 & 1 5 & 0 & 0 8 & 3 & 9 & & sum = 14 Step 3: Calculate Variance. sigma2 = 14/4 = 3.5 So Variance = 3.5 (Option B). The given correctoption 'c' (5.5) is incorrect. Hence, Option B is the correct answer.

Measures of Central Tendency and DispersionMCQMTP Apr 21Question 3172 of 473

All Questions

The variance of the data $\displaystyle 3, 4, 5, 8$ is

Options

\displaystyle 4.5

\displaystyle 3.5

\displaystyle 5.5

\displaystyle 6.5

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Correct Answer

✅ Option b — $\displaystyle 3.5$

All Options:

A $\displaystyle 4.5$
B $\displaystyle 3.5$
C $\displaystyle 5.5$
D $\displaystyle 6.5$

Detailed Solution & Explanation

**Given data:** 3, 4, 5, 8;

\displaystyle n = 4

**Step 1: Calculate Mean.**

\bar{x} = \frac{3+4+5+8}{4} = \frac{20}{4} = 5

**Step 2: Calculate squared deviations.**

\begin{array}{|c|c|c|} \hline x_i & (x_i - 5) & (x_i - 5)^2 \\ \hline 3 & -2 & 4 \\ 4 & -1 & 1 \\ 5 & 0 & 0 \\ 8 & 3 & 9 \\ \hline & & \sum = 14 \\ \hline \end{array}

**Step 3: Calculate Variance.**

\sigma^2 = \frac{14}{4} = 3.5

So Variance = **3.5** (Option B). The given `correct_option` 'c' (5.5) is incorrect. Hence, **Option B** 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

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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The variance of the data 3,4,5,8\displaystyle 3, 4, 5, 83,4,5,8 is