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Measures of Dispersion — Economics STD 11 Commerce — Question

CBSE BoardEnglish MediumSTD 11 CommerceEconomicsMeasures of Dispersion3 Marks
Question
What is the formula of Combined Standard Deviation?
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Answer

If there are two groups containing $n_1$, and $n_2$​​​​​​​, observations, $\bar{\text{X}}_1$ and $\bar{\text{X}}_2,$ as respective arithmetic means and $s_1$, and$ s_2,$ as respective standard deviations, then combined standard deviation is given by$\sigma_{\text{c}}=\sqrt{\frac{\text{n}_1\text{s}^2_1+\text{n}_2\text{s}^2_2+\text{n}_1\text{d}^2_1+\text{n}_2\text{d}^2_2}{\text{n}_1+\text{n}_2}}$
where, $d_1$ and $d_2 $are the differences between individual mean and combined mean of series 1 and series 2 respectively.

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