**Quartiles**

For the **quartile deviation**, let us have an idea about the **quartiles**. We know that the median
divides the given observations arranged in ascending or descending order into
two equal parts. Similarly, the quartiles divide the given observations into
four equal parts after arranging them in ascending or descending order. So
there are three quartiles denoted by Q_{1}, Q_{2} and Q_{3}
known as the **first**, the **second** and the **third quartile** respectively.

If N be the number of observations of discrete data arranged in the ascending or descending order, then the quartiles are given by the following formula:

In the case of continuous frequency distribution, the quartiles are calculated by the following formula:

**Inter Quartiles Range**

__Inter Quartile Range__**:**** **The difference between the
third and the first quartile is called **inter
quartile range**.

i.e. **Inter Quartile Range = Q _{3} – Q_{1}**

**Quartiles Deviations**

The average
of deviation of the first quartile and the third quartile taken from median (M)
is called the **quartile deviation** or **semi-inter quartile range**.

**Coefficient of Quartiles**

As the unit of quartile deviation is same as that of the given
observations, the two distributions with different units cannot be compared by
quartile deviation. To facilitate the comparison of the quartiles of two or
more than two series, a relative measure, the **coefficient of quartile deviation** is used, which is calculated as,

**Worked Out Examples**

**Do you have any questions regarding the Quartile Deviation?**

You can ask your questions or problems here in the comment section below.

calculate lower and upper quartiles, when quartile deviation =10 and co-efficient of quartile deviation=0.5

ReplyDeleteHere is the solution to your problems,

Delete[image src=" https://1.bp.blogspot.com/-sUm0wdOt6QA/YKi3_oi56WI/AAAAAAAAIms/0DJc_EvUlQ8OTOEw1UD9khdnUXtyASZWACLcBGAsYHQ/s16000/Comment%2B1%2Bsolution.png"/]

Comment here if you have more problems regarding the quartile deviation.

Less than30 5 30-40 4 40-50 3 50-60 3 60-70 5 find quartile deviation

ReplyDeleteHere is the solution to your problems,

Delete[image src=" https://1.bp.blogspot.com/-PcJa57QPEOM/YNIDJ1zcEKI/AAAAAAAAJSg/vrjKeeO9lVQvOVIq3rfqe-IoUPtKSrzFQCLcBGAsYHQ/s16000/Comment%2B2%2Bsolution.png"/]

Comment here if you have more problems regarding the quartile deviation.