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SAI International School
CLASS - X

Mathematics
CHAPTER-14: Statistics

Lesson Notes-3

SUBTOPIC : Median of Grouped Data

Median and Cumulative Frequency

Median is one of the measure of central tendency

Median: Median is defined as the middle most or central observation, when the
observation are arranged either in ascending or descending order of their magnitudes.

Median divides the arranged series into two equalparts,i.e.50% of the observations lie
below the median and the remaining are above the median.

Let n be the total number of observations and let they are arranged in ascending or
descending order.

Median of the data depends on the number of observations( N )

 N 1  th
Case-1-If n is odd then Median = Value of   observation
 2 

 N  th  N 1  th
Case-2-If n is even, then Median = Mean of value of   and   observations
 2   2 

 1   N  th  N  th
=   x Value of [      1 ] observations
 2   2   2 

Example-1:Calculate the median of the following numbers.
6, 3, 7, 5, 4, 4, 6, 8, 4, 5, 3.

Solution: Arranging the numbers in ascending order we have,
3, 3, 4, 4, 4, 5, 5, 6, 6, 7, 8
Number of terms = 11 here N =11=odd number
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