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To compute the median of a grouped data set, follow the steps given below:

1 Step 1. Determine the rank of the median that is given by

2 Step 2. Locate the class containing the median and then proceed as follows:Add the frequencies of classes starting from class 1 and continue until the sum becomes greater than or equal to . Then, the class containing the median is identified.

3 Step 3. Once we identify the class containing the rank of the median, then the median is given by(2.6.3)

where

  lower limit of the class containing the median

 

  frequency of the class containing the median

  class width of the class containing the median

Example 2.6.2 (Median of a grouped data) Find the median of the grouped data in Example 2.6.1.

Solution:

1 Step 1. Rank of the median .

2 Step 2. Add the frequencies until the sum becomes greater than or equal to 20.5, that is,Stop at the class whose frequency is 6, so that the class containing the median is .

3 Step 3. Using (2.6.3), we have