Category: Quartile

REFLECTION: FOR STUDENTS: A good rule in organizational analysis is that no meeting of the minds is really reached until we talk of specific actions or decisions. We can talk of who is responsible for budgets, or inventory, or quality, but little is settled. It is only when we get down to the action words-measure, compute, prepare, check, endorse, recommend, approve-that we can make clear who is to do what. -Joseph M. Juran

FOR ACADEMICS: Without a standard there is no logical basis for making a decision or taking action. -Joseph M. Juran

FOR PROFESSIONALS/PRACTITIONERS: Both pure and applied science have gradually pushed further and further the requirements for accuracy and precision. However, applied science, particularly in the mass production of interchangeable parts, is even more exacting than pure science in certain matters of accuracy and precision. -Walter A. Shewhart

Foundation

When we left this small series on basic QA statistics, we had just discussed basic measures of Dispersion- Range, Variance, and Standard Deviation. As promised, we are now covering the basics of Interquartile Range (IQR for short). IQR is also a measure of dispersion, but as I’m sure you will be exposed to IQR in the future, I thought it best to give it a separate post.
The IQR range, like the other measures of dispersion, is used to measure the spread of the data points in a data set. IQR is best used with different measurements like median and total range to build a complete picture of a data set’s tendency to cluster around its mean. IQR is also a very useful tool to use to identify outliers (values abnormally far from the mean of a data set), but do not worry about the more in-depth math.

First, to Define all of the aspects of IQR

-First Quartile (Q1)- The value at which 25% of the data are less than or equal to this value (does not have to be a value in the data set).

-Second Quartile (Q2)- The value at which 50% of the data are less than or equal to this value. It is also known as the median. The second quartile or median does not have to be a value in the data set.

-Third Quartile (Q3)- This is the point at which 75% of the data are less than or equal to this value. It also does not have to be in the data set.

-Fourth Quartile (Q4)- This value is the maximum value in the data set (100% of the data are less than or equal to this value).

-Interquartile Range (IQR)- IQR is the Third Quartile minus the First Quartile and considered a measure of dispersion.

(Kubiak, 2017)

Calculating Quartiles

There are several methods for calculating quartiles, so the technique I am going to use is just what I consider the most basic without delving into any more in-depth math.

Steps:

• Order the data set from smallest to largest.
• Determine the median (reference my post: Basic QA Statistics Series(Part 2)- Basic Measures of Central Tendency and Measurement Scales). 
• This determination separates the data into two sets (an upper half and lower half). This Median is Q2
• The First Quartile (Q1) is found by determining the median of the lower half of the data (not including the Median from the previous step when calculating the lower half data set median).
• Q3 is the median of the upper half of the data set, not including the value for Q1 in the top half median determination
• Q4 is the maximum in the data set.

(Kubiak, 2017)

Conclusion

As you can see, I stacked the data deck with a massive outlier in the data set. 1000 is far from the mean, but the IQR is not affected by this enormous outlier, as it only takes into account Q1 and Q3.
This property of IQR helps prevent outliers from convincing you the mean is just fine, when in fact, the entire system may be out of whack but compensated for by outliers in your data. The little chart you see is called a Box and Whisker plot, and we will give it a separate post later after we discuss Histograms in the nest post.

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