Find the mean of the following data:

Values (X) = 19, 21, 23, 25, 27, 29, 31

Frequencies (f) = 13, 15, 16, 18, 16, 15, 13

​$$\begin{array}{|c|c|c|}\hline\bf\text{X} &\bf f &\bf f\cdot X \\\hline19&13& 247 \\\hline21&15&315 \\\hline23&16&368\\\hline25&18&450\\\hline27&16&432\\\hline29&15&435\\\hline31&13&403\\\hline& \bf\sum{f} = 106 & \bf \sum{f \cdot X} = 2650 \\\hline\end{array}$$​​

Now,

Mean = $$\text{Mean} = \frac{\sum f \cdot X}{\sum f} = \frac{2650}{106} = \bf 25$$​​

Thus, Mean of the data set is 25.​