Calculate the median for an exclusive (continuous) distribution given below.
Class Interval Frequency
$10 - 20$ $11$
$20 - 30$ $13$
$30 - 40$ $13$
$40 - 50$ $9$
$50 - 60$ $4$

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Solution

We first prepare the cumulative frequency table (see above).
Class Interval Frequency (f) Cumulative frequency $(f_{c})$
$10 - 20$ $11$ $11$
$20 - 30$ $13$ $24$
$30 - 40$ $13$ $37$
$40 - 50$ $9$ $46$
$50 - 60$ $4$ $50$
Here we see that the total number of observation is $N = 50$ . Therefore $(30 - 40)$ is the median class. We also observe that $L R L = 30, f_{c} = 24, f_{m} = 13$ and $i = 20 - 10 = 10$ . Now we are in a position to use the formula for median:
$m e d i a n = L R L = \frac{(\frac{N}{2}) - f x}{f m} \times i = 30 + \frac{(25 - 24)}{13} \times 10 = 30 + \frac{10}{13} = 30.77$ approximately.

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