**Question:**

The following table gives the frequency distribution of married women by age at marriage:

Calculate the median and interpret the results.

**Solution:**

Here, the frequency table is given in inclusive form. So, we first transform it into exclusive form by subtracting and adding *h*/2 to the lower and upper limits respectively of each class, where *h* denotes the difference of lower limit of a class and upper limit of the previous class.

We have, *N* = 357

So, *N*/2 = 178.5

Thus, the cumulative frequency just greater than 178.5 is 193 and the corresponding class is 19.5−24.5.

Therefore, 19.5−24.5 is the median class.

Here, *l* = 19.5, *f *= 140, *F* = 193* *and *h* = 5

We know that

Median $=l+\left\{\frac{\frac{N}{2}-F}{f}\right\} \times h$

$=19.5+\left(\frac{178.5-53}{140}\right) \times 5$

$=19.5+\frac{125.5}{140} \times 5$

$=19.5+\frac{125.5}{28}$

$=\frac{546+125.5}{28}$

$=23.98$

Hence, the median age 23.98 years.

Thus, nearly half the women were married between the age of 19.5 years and 24.5 years.