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

Step 1: State the formula for the mean age.
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.

Step 2: List the data from the table.

Step 3: Calculate the total number of girls, $\sum f_i$.
$\sum f_i = 3 + 4 + 2 + 5 + 1$
$= 7 + 2 = 9$
$9 + 5 = 14$
$14 + 1 = 15$
Total number of girls $= 15$.

Step 4: Calculate the total age sum, $\sum (x_i \cdot f_i)$ (in years).
$11 \times 3 = 33$
$12 \times 4 = 48$
$13 \times 2 = 26$
$14 \times 5 = 70$
$15 \times 1 = 15$
$\sum (x_i \cdot f_i) = 33 + 48 + 26 + 70 + 15$
$33 + 48 = 81$
$81 + 26 = 107$
$107 + 70 = 177$
$177 + 15 = 192$
Total age sum $= 192$ years.

Step 5: Calculate the mean age.
$\bar{x} = \frac{192}{15}$
$15 \times 12 = 180$
$192 - 180 = 12$
$\frac{12}{15} = 0.8$
$\bar{x} = 12 + 0.8 = 12.8$ years.

The mean age of the girls is $12.8$ years.
12.8