## Median

The median is the value of the middle most observation when the data are arranged in ascending or descending order of their magnitude.

Look at the example below:

In the above series, the numbers are arranged in ascending order. Here the fourth item ‘4’ has 3 items before it and 3 items after it, so 4 is the middle term, and hence 4 is the median of the given series.

Median can be calculated by using the following steps:

### Median for individual data:

We can find median for individual data by using the following formula,

### Median for discrete data:

The repeated data, which have the frequency is called discrete data. To calculate the median of repeated data, we follow the following steps:

1.  Draw a table with three columns.
2.  Write down the items (x) in ascending order in the first column.
3.  Write the corresponding frequency (f) of each item or object in the second column.
4.  Write the cumulative frequency in the third column

### Median for grouped data:

The data given in the class-interval is called grouped data. To calculate the median of grouped data, we follow the following steps:

1.  Draw a table with three columns.
2.  Write down the class-intervals in ascending order in the first column.
3.  Write the corresponding frequency (f) of each item or object in the second column.
4.  Write the cumulative frequency in the third column
6.  Write down the value of L (lower limit) and f (frequency) of the median class, c.f. (cumulative frequency) of the preceding class and i (height of class-interval). Then find the value of median by using the formula given below:

### Workout Examples

Example 1: Find the median of: 2, 7, 10, 16, 8, 9, 15

Solution: Here,
Data in ascending order: 2, 7, 8, 9, 10, 15, 16
No. of data (N) = 7
Median = ?
We know,

Example 2: Find the median of: 7, 5, 9, 3, 2, 1, 10, 8

Solution: Here,
Data in ascending order: 1, 2, 3, 5, 7, 8, 9, 10
No. of data (N) = 8
Median = ?
We know,

Example 3: Calculate the median of the data given in the table.

 x 60 70 80 90 100 f 2 4 6 8 1

Solution: Here,

 x f c.f. 60 70 80 90 100 2 4 6 8 1 2 6 12 20 21 N = 21

We know,

Example 4: Calculate the median of the data given in the table.

 Marks 0-10 10-20 20-30 30-40 40-50 No. of students 5 20 10 15 7

Solution: Here,

 x f c.f. 0-10 10-20 20-30 30-40 40-50 5 20 10 15 7 5 25 35 50 57 N = 57

We know,

You can comment your questions or problems regarding the median here.