The table below shows the ages of a group of girls who were born in March. What is the mean age of the girls?

The mean age $\bar{x}$ (in years) is given by

$$\bar{x} = \frac{\sum (x_i \cdot f_i)}{\sum f_i}$$

where $x_i$ is the age in years and $f_i$ is the number of girls of that age.

$$\sum f_i = 3 + 4 + 2 + 5 + 1$$ $$= 7 + 2 = 9$$ $$9 + 5 = 14$$ $$14 + 1 = 15$$

Total number of girls $= 15$.

$$11 \times 3 = 33$$ $$12 \times 4 = 48$$ $$13 \times 2 = 26$$ $$14 \times 5 = 70$$ $$15 \times 1 = 15$$ $$\sum (x_i \cdot f_i) = 33 + 48 + 26 + 70 + 15$$ $$33 + 48 = 81$$ $$81 + 26 = 107$$ $$107 + 70 = 177$$ $$177 + 15 = 192$$

Total age sum $= 192$ years.

$$\bar{x} = \frac{192}{15}$$ $$15 \times 12 = 180$$ $$192 - 180 = 12$$ $$\frac{12}{15} = 0.8$$

$\bar{x} = 12 + 0.8 = 12.8$ years.

The mean age of the girls is 12.8 years.
12.8