# Quartile Deviation ## 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 Q1, Q2 and Q3 known as the first, the second and the third quartile respectively.

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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 = Q3 – Q1

### 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.

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

1. Here is the solution to your problems,
[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.

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

1. Here is the solution to your problems,
[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.

3. length in hours:700-900 900-100 1100-1300 1300-1500
samples: 10 16 26 8
find out standard deviation by step deviation method

1. Calculation of Standard Deviation by step-deviation method: [image src="https://blogger.googleusercontent.com/img/a/AVvXsEiZGHMpZWSgApdWNIe0fMnb3nOvmAhq8-U0gxqON9jZx9x9JKRnjjr5aSt9uIxANXU4TE2fz9QXoajPLYHyxEjbTua6dTilTVDTLFtZ4NGH-mfOwIiq84II3O6ESeQvj100F6zmlrgbpyxQ_Ky9uKZ9hJXD_7Hdsj642wpVowX3HOJLMKLL4oHX_Bc41Q=s16000 "/]
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4. Please do one question in which ci is given like 0 to 10. 0 to 20. 0 to 40.

1. We have to change the class intervals into 0-10, 10-20, 20-30… and filter the frequency values accordingly and then find quartile deviation. You can post your question here.

5. In symmetric distribution 50% of the items are above 60 and 75% of the items are below 75. Therefore, the coefficent of quartile is ---- and the coefficient of skewness is -----

6. 17,2,7,27,15,5,14,8,10,24,48,10,8,7,18,28 pls solve that problem