Central Tendency & DispersionPYQ Jan. 21Question 3003 of 454
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If there are two groups with n1\displaystyle n_1 and n2\displaystyle n_2 observations and H1\displaystyle H_1 and H2\displaystyle H_2 are respective harmonic means, then the harmonic mean of combined observation is

Options

An1H1+n2H2n1+n2\displaystyle \frac{n_1 H_1 + n_2 H_2}{n_1 + n_2}
Bn1H1+n2H2H1+H2\displaystyle \frac{n_1 H_1 + n_2 H_2}{H_1 + H_2}
Cn1+n2n1H1+n2H2\displaystyle \frac{n_1 + n_2}{\frac{n_1}{H_1} + \frac{n_2}{H_2}}
D(n1+n2)H1H2n1H1+n2H2\displaystyle \frac{(n_1 + n_2)H_1 H_2}{n_1 H_1 + n_2 H_2}
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Correct Answer

Option an1H1+n2H2n1+n2\displaystyle \frac{n_1 H_1 + n_2 H_2}{n_1 + n_2}

All Options:

  • An1H1+n2H2n1+n2\displaystyle \frac{n_1 H_1 + n_2 H_2}{n_1 + n_2}
  • Bn1H1+n2H2H1+H2\displaystyle \frac{n_1 H_1 + n_2 H_2}{H_1 + H_2}
  • Cn1+n2n1H1+n2H2\displaystyle \frac{n_1 + n_2}{\frac{n_1}{H_1} + \frac{n_2}{H_2}}
  • D(n1+n2)H1H2n1H1+n2H2\displaystyle \frac{(n_1 + n_2)H_1 H_2}{n_1 H_1 + n_2 H_2}

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