 Krishna
0

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