Harmonic mean of $$$11$$$, $$$13$$$
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Find the harmonic mean of $$$11$$$, $$$13$$$.
Solution
The harmonic mean of data is given by the formula $$$H = \frac{n}{\sum_{i=1}^{n} \frac{1}{x_{i}}}$$$, where $$$n$$$ is the number of values and $$$x_i, i=\overline{1..n}$$$ are the values themselves.
Since we have $$$2$$$ points, $$$n = 2$$$.
The sum of the reciprocals of the values is $$$\frac{1}{11} + \frac{1}{13} = \frac{24}{143}$$$.
Therefore, the harmonic mean is $$$H = \frac{2}{\frac{24}{143}} = \frac{143}{12}$$$.
Answer
The harmonic mean is $$$\frac{143}{12}\approx 11.916666666666667$$$A.