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MEDIAN OF A GROUPED DATA
MEDIAN : It is a measure of central tendency which gives the value of the middle most observation in the data. In a grouped data, it is not possible to find the middle observation by looking at the cumulative frequencies as the middle observation will be some value in a class interval. It is, therefore, necessary to find the value inside a class that divides the whole distribution into two halves.
MEDIAN CLASS : The class whose cumulative frequency is greater than (N/2) is called the median class.
To calculate the median of a grouped data, we follow the following steps :
STEP1 :Prepare the cumulative frequency table corresponding to the given frequency distribution and obtain
STEP2 :Find (N/2)
STEP3 :Look at the cumulative frequency just greater than (N/2) and find the corresponding class (Median class).
STEP4 :Use the formula Median,
Where = Lower limit of median class.
f = Frequency of the median class.
C = Cumulative frequency of the class preceding the median class.
h = Size of the median class.
Ex.10 Find the median of the following frequency distribution :
Sol. At first we prepare a cumulative frequency distribution table as given below :
The cumulative frequency just greater than 50 is 64 and the corresponding class is 2030.
So, the median class is 2030.
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