Question

Method to find the median of grouped data

Answer 1

Use the following calculations tofind the median for a groupedfrequency distribution. Figure outwhich interval contains themedian by using the (n + 1) ÷ 2 formula. Take whatever value thecalculation gives you and then add up the numbers in the frequency column until you come to that value 

Answer 2

MEDIAN OF GROUPED DATA

MEDIAN

Median is that value of the given number of observations which divides it into exactly two equal parts when the data is arranged in ascending or descending order .

METHOD TO FIND THE MEDIAN

To find the median of the given data, we follow the following steps:

STEP 1 . Arrange the data in an ascending (increasing) or a descending (decreasing) order of magnitude.

STEP 2. Find the total number of observations. Let n be the total number of observations.

STEP 3. Two cases arise:

CASE I : When n is odd, then

median = value of (n + 1/2)th

observation.

CASE 2: When n is even, then

median = mean of (n/2)th

and (n/2) + 1 th observations.

ILLUSTRATION. The weights of 10 students (in key are: 45, 60, 38, 37, 52, 55, 31, 44, 49, 36. Find the median weight.

SOLUTION. Arranging the weights in an ascending order, we get

31, 36, 37, 38, 44, 45, 49, 52, 55, 60.

Here, n = 10 (= even)

∴ Median weight = mean of (10/2)th and (10/2)+1 th term

= mean of 5th and 6th term

= mean of 44 and 45

= (44+45)/2 kg = 44.5 kg

Hence, the median weight = 44. 5 kg.

MEDIAN OF DISCRETE FREQUENCY DISTRIBUTION

To find the median of the given data, we follow the following steps:

STEP 1. Arrange the terms in an ascending or a descending order.

STEP 2. Prepare a cumulative frequency table.

STEP 3. Let the total frequency be n

Two cases arise:

CASE I : When n is odd, then

median = value of (n + 1/2)th

observation.

CASE 2: When n is even, then

median = mean of (n/2)th and

(n/2) + 1 th observations.