##
**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__**:**

__Median for individual data__

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

###
__Median
for discrete data__**:**

__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__**:**

__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*

*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. |

60708090100 |
24681 |
26122021 |

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. |

0-1010-2020-3030-4040-50 |
52010157 |
525355057 |

N = 57 |

*We know,*

*You can comment your questions or problems regarding the*

**median**here.
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