Statistics

Question

The variance of data set 2, 4, 6 is

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1. **Find Mean**: $\bar{x} = \frac{2+4+6}{3} = \frac{12}{3} = 4$.
2. **Deviation Calculation**: $(x_i - \bar{x})$
   - $(2-4) = -2 \implies (-2)^2 = 4$
   - $(4-4) = 0 \implies (0)^2 = 0$
   - $(6-4) = 2 \implies (2)^2 = 4$
3. **Apply Variance Formula**: $Var(X) = \frac{\sum (x_i - \bar{x})^2}{n}$.
4. **Calculation**:
   - $Var = \frac{4 + 0 + 4}{3} = 8/3$.
5. **Note**: Standard deviation would be $\sqrt{8/3}$.

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