If harmonic mean of first 5 observations is $\frac{5}{2}$and  harmonic mean of another 5 observations is $\frac{9}{2}$then harmonic mean of all 10 observations is

Let H₁, and n₁, are the harmonic mean and number of
observations of first group and H₂and n₂ are the
harmonic mean and number of observations of another
group.
$\therefore$ By using combined harmonic mean formula, we get
combined harmonic mean $\begin{array}{l}=\frac{{\mathrm{n}}_1+{\mathrm{n}}_2}{\frac{{\mathrm{n}}_1}{{\mathrm{H}}_1}+\frac{{\mathrm{n}}_2}{{\mathrm{H}}_2}}=\frac{5+5}{\frac{5}{5}+\frac{5}{9}}\\ =\frac{10}{\frac{28}{9}}=\frac{90}{28}=\frac{45}{14}\end{array}$