maths > statistics-basics

Median of Group Data

what you'll learn...

overview

In this page, finding median of grouped data is explained with some examples.

recap

Median of a data is, the value that has equal number of smaller and larger data values in the given data.

Consider the data: Number of pens carried by 10 students.

$1,2,1,2,2,3,2,2,3,2$$1 , 2 , 1 , 2 , 2 , 3 , 2 , 2 , 3 , 2$

The median of the data is computed as follows.
arrange the data in ascending order = $1,1,2,2,2,2,2,2,3,3$$1 , 1 , 2 , 2 , 2 , 2 , 2 , 2 , 3 , 3$
count / number of data values $=10$$= 10$
Find the position of middle value $\frac{10}{2}=5$$\frac{10}{2} = 5$. So the avaerage of data values in position $5$$5$ and $6$$6$ is the median.

Median $=\frac{2+2}{2}$$= \frac{2 + 2}{2}$ $=2$$= 2$

finding median using frequency

Consider the data given in the table in frequency form. To compute the median, the frequency of the data values can be used.

Considering the data given in the table. The calculation of median is illustrated in the table. It is noted that the median computed using the frequency form and the median computed using the raw data are identical.

median of grouped-data

Consider the grouped data given in the figure. Let us study how median can be computed for grouped data.

Computing median of grouped data is given in the table.

The last column provides the cumulative frequency. The average of data values in positions $10$$10$ and $11$$11$ is the median class of this data. So the median class is $90-95$$90 - 95$

Note that the height value or the class mark values are arranged in the ascending order while computing the median.

Another example of computing median class of grouped data is given in the table.

summary

Computing Median of Grouped Data : Arrange the classes in ascending order and the class-mark of the class having center of the data is the median.

Outline