JEE MainMathematicsModerateStatistics

The standard deviations of two sets containing 10 and 20 members
are 2 and 3, respectively measured from their common mean 5. The SD for
the whole set of 30 members is

Show answer and solution

\sigma = \sqrt{\frac{n_{1}\left( \sigma_{1}^{2} + d_{1}^{2} \right) + n_{2}\left( \sigma_{2}^{2} + d_{2}^{2} \right)}{n_{1} + n_{2}}} = \sqrt{\frac{22}{3}}

Source: Grass-G / M-23 Mathematics Paper 31 Dec FST.docx

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