Question

Write the formula to find the median for grouped data and explain each term.

Answer 1

Hint: Median of a grouped data is given by \[median = l + \left( {\dfrac{{\dfrac{n}{2} - cf}}{f}} \right) \times h\]. This formula of median for grouped data is similar to the formula of mode in an interval. Here, \[l\] represent the lower limit of the median class, \[n\] represents the total sum of all frequencies, \[cf\] represent the cumulative frequency before the median class, \[f\] represent the frequency of the median class and \[h\] represents the class width.

Complete step-by-step answer:
The formula for median in a grouped data is \[median = l + \left( {\dfrac{{\dfrac{n}{2} - cf}}{f}} \right) \times h\], where \[l\] represent the lower limit of the median class, \[n\] represents the total sum of all frequencies, \[cf\] represent the cumulative frequency before the median class, \[f\] represent the frequency of the median class and \[h\] represents the class width.
Median of a data set represents the middle value, when the data is arranged in ascending order. It generally helps in determining the most likely value of the data set, but only if the distribution of data is continuous. The value of the median should have the highest frequency for a symmetrical distribution of data. However, if the distribution of the data is unsymmetrical or skewed, median doesn’t represent the most likely value as there will be an extremely high or an extremely low value as compared to the rest of data.

Note: The median of a given set of discrete data can be found out by simply arranging it into ascending order and then picking out the middle value. However for a grouped data, we have to use the formula of median used above. It is best for a student to be well versed with these formulae.