Median

Median of a group of observation is the value which lies in the middle of the data (when arranged in an ascending or descending order) with half of the observations above it and the other half below it.

● When the number of observations (n) is odd.

Then, median is (n + 1)/2 ^th observation.

● When the number of observations (n) is even.

Then median is the mean of (n/2)^th and (n + 1/2)^th observation.

i.e., Median =

Let us observe the following solved problems using step-by-step explanation.

Worked-out examples on median:

1. Find the median of the data 25, 37, 47, 18, 19, 26, 36.

Solution:

Arranging the data in ascending order, we get 18, 19, 25, 26, 36, 37, 47

Here, the number of observations is odd, i.e., 7.

Therefore, median = (n + 1/2)^th observation.

                         = (7 + 1/2)^th observation.

                         = (8/2)^th observation

                         = 4^th observation.

4^th observation is 26.

Therefore, median of the data is 26.

2. Find the median of the data 24, 33, 30, 22, 21, 25, 34, 27.

Solution:

Here, the number of observations is even, i.e., 8.

Arranging the data in ascending order, we get 21, 22, 24, 25, 27, 30, 33, 34

Therefore, median = {(n/2)^th observation + (n + 1/2)^th observation}/2

                         = (8/2)^th observation + (8/2 + 1)^th observation

                         = 4^th observation + (4 + 1)^th observation

                         = {25 + 27}/2

                         = 52/2

                         = 26

Therefore, the median of the given data is 26.

● Statistics

• Real Life Statistics
  
• Terms Related to Statistics
  
• Frequency Distribution of Ungrouped and Grouped Data
  
• Use of Tally Marks
  
• Class Limits in Exclusive and Inclusive Form
  
• Construction of Bar Graphs
  
• Mean
  
• Mean of the Tabulated Data
  
• Mode
  
• Median
  
• Construction of Pie Chart
  
• How to Construct a Line Graph?
  

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