why we use cumulative frequency table to find median of any given grouped data? I mean what is the logic behind this??

Asked by Ayush Maurya | 29th Jun, 2013, 05:00: PM

Expert Answer:

The median is defined as the number in the middle of a given set of numbers arranged in order of increasing magnitude. When given a set of numbers, the median is the number positioned in the exact middle of the list when you arrange the numbers from the lowest to the highest. 
 
So, now since you want to identify the exact middle number that is the number which occurs at mth place with m~n/2 where n is the total number of observations (sum of frequency). Constructing a cumulative frequency table will help you easily identify as to which data point corresponds to 50% of the total frequency. This is the reason why it is used to find the median of any given grouped data, where you have frequencies given. 

Answered by  | 29th Jun, 2013, 05:17: PM

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