To find the median of a grouped data, we need to find the cumulative frequency and
Then we have to find the median class, which is the class of the cumulative frequency near or greater than the value of .
Cumulative Frequency is calculated by adding the frequencies of all the classes preceding the given class.
Then substitute the values in the formula
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
Find the median of the given table.
|Class Interval||Frequency||Cumulative Frequency (fc)|
|1 – 5||4||4||4|
|6 – 10||3||7||4 + 3 = 7|
|11 – 15||6||13||7 + 6 = 13|
|16 – 20||5||18||13 + 5 = 18|
|21 – 25||2||20||18 + 2 = 20|
|N = 20|
The median class is 11 – 15 as its cumulative frequency is 13 which is greater than 10.
The empirical relation between the three measures of central tendency is 3 Median = Mode + 2 Mean