## Median Data

The variable values dividing the total set of observations into two equal parts of the data is called the median data.

For a data set, it may be thought of as the “middle” value.

For example, in the data set [1,3,3,6,7,8,9], the median is 6, the fourth largest, and also the fourth smallest, number in the sample.

### For Individual Series

- First, we change the data in ascending or descending order of their magnitude.
- If the number of observations is odd, then the middle value gives the median among all the data.
- Again, if the number of observations is even then there will be two middle values, the average of two middle values gives the median.
- The formula for computing the median in case of individual series is given by

where,

n=Number of Observations

### For discrete series,

- Arrange the data in ascending order of their magnitude.
- From the cumulation frequency table.
- Find the value of .
- See the cumulation frequency table equal to or just greater than .
- Note the corresponding value of x which gives the value of the median.

where,

N=Number of Observations

### For Continuous Series,

- Prepare a c.f. table.
- Find
- See if the value in c.f. the table is equal to or greater than , note the class.
- The corresponding class contains the value of the median and is called the median class.
- The following formula is used in finding the median:

where

l=lower limit of the median class

f=frequency of the median class

c.f.=c.f. of preceding median class

h=size of the median class

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