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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
For two datasets each of size $5$, variances are $4$ and $5$ and means are $2$ and $4$ respectively.
The variance of the combined dataset is:
Solution
Let $n_1 = n_2 = 5, ; \sigma_1^2 = 4, ; \sigma_2^2 = 5, ; \bar{x}_1 = 2, ; \bar{x}_2 = 4$ Then $\sigma^2 = \dfrac{n_1\sigma_1^2 + n_2\sigma_2^2}{n_1+n_2} + \dfrac{n_1(\bar{x}_1 - \bar{x})^2 + n_2(\bar{x}_2 - \bar{x})^2}{n_1+n_2}$ where $\bar{x} = \dfrac{n_1\bar{x}_1 + n_2\bar{x}_2}{n_1+n_2} = 3$ $\Rightarrow \sigma^2 = \dfrac{5(4) + 5(5)}{10} + \dfrac{5(1)^2 + 5(1)^2}{10}$ $= 4.5 + 1 = 5.5 = \boxed{11/2}$Online Test Series, Information About Examination,
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