The median value of a set of data is the middle value of the ordered data. That is, the data must be put in numerical order first. The “Median” of a data set is dependant on whether the number of elements in the data set is odd or even.Watch MEDIAN to learn more.
First reorder the data set from the smallest to the largest then if the number of elements are odd, then the Median is the element in the middle of the data set. If the number of elements are even, then the Median is the average of the two middle terms.
Odd Number of Elements
Data Set = 2, 5, 9, 3, 5, 4, 7
Reordered = 2, 3, 4, 5, 5, 7, 9
Median = 5
Even Number of Elements
Data Set = 2, 5, 9, 3, 5, 4
Reordered = 2, 3, 4, 5, 5, 9
Median = ( 4 + 5 ) / 2 = 4.5
To determine the median of ungrouped data with N elements, one should first order the data from lowest to highest. The median is determined by finding either the middle element in the data or the average of the middle two elements, depending on whether there are an odd or even number of elements in the data.
Grouped data is data that has been organized into classes. Grouped data has been classified and some data analysis has been done, which means this data is no longer raw. Un-grouped data has not been organized into groups. It is just a list of numbers.
(i) Arrange the data in ascending or descending order of magnitude.
(ii) Find out the cumulative frequencies.
(iii) Apply the formula median= size of (N + 1)/2
(iv) Now look at the cumulative frequency column and find that total which is either equal to (N + 1)/2 or next higher to that and determine the value of the variable corresponding to it. That gives the vbalue of median.
Useful for CBSE, ICSE, NCERT & International Students
Grade : 9
Subject : Maths
Lesson : Statistics
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