Central Tendency & DispersionMTP Apr 21Question 3172 of 473

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

Options

A

\displaystyle 4.5

B

\displaystyle 3.5

C

\displaystyle 5.5

D

\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.

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