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MathematicsStatisticsRelation Between Variance and Mean DeviationMedium2 minPYQ_2024

MathematicsMediumsingle choice

If the variance of the data $2, 3, 5, 8, 12$ is $σ^{2}$ and the mean deviation from the median for this data is M , then $σ^{2} - M =$

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Solution:

Observations : $2, 3, 5, 8, 12$ Mean $= \frac{2 + 3 + 5 + 8 + 12}{5} = 6$ $∴ σ^{2} = 13.2$ Median $= 5 = m$ $∴$ Mean deviation about median $\Rightarrow \frac{Σ ∣ x _{i} - m ∣}{n} = \frac{3 + 2 + 0 + 3 + 7}{5} = 3$ $M = 3 \Rightarrow σ^{2} - M = 13.2 - 3 = 10.2$

Stream:BITSATSubject:MathematicsTopic:StatisticsSubtopic:Relation Between Variance and Mean Deviation

⏱ 2mℹ️ Source: PYQ_2024

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