>>Return to Tell Me About Statistics!
In this article, we will discuss quartile range and quartile deviation.
When arranging the data from smallest to largest, one-fourth of the minimum value is the first quartile, the point in the middle is the median, and one-fourth of the maximum value is the third quartile.
The difference between the first and third quartiles is called the quartile range and half of the quartile range is called the quartile deviation. Similar to standard deviation, it is an indicator of population variation.
If either the quartile range or quartile deviation is large, the data can be said to have large variability. The standard deviation is affected by extremely large or small values (outliers), but the quartile range and quartile deviation are less impacted, since they are determined by 50% of the central data.
How to find the quartile deviation
Using the data in Table 1, we find the quartile deviations for datasets A and B.
[Table 1]
To determine the quartile deviation, you must first obtain the quartile range.
[Formula]
quartile range = third quartile – first quartile
quartile deviation = quartile range ÷ 2
[Quartile deviation of Data A and B]
quartile range = 5.00-3.00 = 2.00
quartile deviation = 1.00
As a result, the quartile deviation of data A and B is 1.00, indicating that the extremely large value (outlier) “100” in data A is not affected.
Notes on quartile range and quartile deviation
Looking at the above example, there is a large difference in the standard deviations; however the quartile deviations are the same. This is because the indicator quartile range and deviation are less susceptible to values larger or smaller (outliers) than the standard deviation. Again, the larger the quartile range and quartile deviation, the greater the variability in the data.
However, the quartile range and quartile deviation data scatter are values near the median, and the variance and standard deviation data scatter are values near the mean. Note that even if one says data variation, the two have different meanings.
Trivia
The first quartile is also called the “lower hinge,” and the third quartile is called the “upper hinge.” The reason why it is called “hinge” is that it is originally a hinge, and it is said that the box-and-whisker plot looks like a hinge.
>>Return to Tell Me About Statistics!
Comments are closed