Median of Grouped Data

To find the median of a grouped data, we need to find the cumulative frequency and \dfrac{n}{2}

Then we have to find the median class, which is the class of the cumulative frequency near or greater than the value of \dfrac{n}{2} .

Cumulative Frequency is calculated by adding the frequencies of all the classes preceding the given class.

Then substitute the values in the formula

Median =1+\left(\dfrac{\dfrac{n}{2}-cf}{f}\right)\times h

where l = lower limit of median class

n = no. of observations

cf = cumulative frequency of the class preceding to the median class

f = frequency of the median class

h = size of class

Example

Find the median of the given table.

Class IntervalFrequencyCumulative Frequency (fc) 
1 – 5444
6 – 10374 + 3 = 7
11 – 156137 + 6 = 13
16 – 2051813 + 5 = 18
21 – 2522018 + 2 = 20 
 N = 20  

Solution

n=20 , so \dfrac{n}{2}=\dfrac{20}{2}=10

The median class is 11 – 15 as its cumulative frequency is 13 which is greater than 10.

Median  =1+\left(\dfrac{\dfrac{n}{2}-cf}{f}\right)\times h

=11+\dfrac{10-7}{6}\times 5

13.5

The empirical relation between the three measures of central tendency is 3 Median = Mode + 2 Mean

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