Step 1: Recall the formula of the median for grouped data.
Median = l + \frac{\frac{n}{2} + cf}{f} * h
where, l = lower boundary of median class,
n = number of observations,
cf = cumulative frequency of class preceding the median class,
f = frequency of median class,
h = class size (size of the median class).
Step 2: Set up a cumulative frequency distribution table
NOTE: The cumulative frequency is calculated using a frequency
distribution table.
Step 3: Calculate the median class of the data.
NOTE: Locate the class whose cumulative frequency exceeds
\frac{n}{2} for the first time. This is called the median class.
The total number of observations n = 400
\frac{n}{2}=\frac{400}{2}\ =\ 200
3000 - 13500 is the class whose cumulative frequency is 216 greater than
(and nearest to) \frac{n}{2}, i.e., 50.
Therefore, 3000 - 3500 is the median class
Step 4: Substitute that values in the median formula
From the table;
l = lower boundary of median class = 3000,
n = number of observations = 400,
cf = cumulative frequency of class preceding the median class = 130
f = frequency of median class = 86
h = class size (size of the median class) = 3500 - 3000 =.500
Substituting the values
Median = l + \frac{\frac{n}{2}-cf}{f}*h
Median = 3000+\frac{200-130}{86}*500
= 3000+406.97
= 3409.97
Hence, the median = 3406.97
