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 = 100
\frac{n}{2}=\frac{100}{2}
125 - 145 is the class whose cumulative frequency is 86 greater than
(and nearest to) \frac{n}{2}, i.e., 50.
Therefore, 35 - 45 is the median class
Step 4: Substitute that values in the median formula
From the table;
l = lower boundary of median class = 35,
n = number of observations = 100,
cf = cumulative frequency of class preceding the median class = 45
f = frequency of median class = 33
h = class size (size of the median class) = 20 - 15 = 5.
Substituting the values
Median = l + \frac{\frac{n}{2}-cf}{f}*h
Median = 35 + \frac{50 - 45 }{33}*5
= 35 + \frac{25}{33}
= 35 + 0.75
Hence, the median = 35.75
