What Are And How To Calculate Quartiles, The Interquartile Range, IQR, And Outliers Explained
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- Опубликовано: 30 июл 2024
- In this video we discuss what are and how to calculate quartiles, the interquartile range, IQR, and Outliers. We use the IQR to determine any possible outliers in a data set.
Transcript/notes
Quartiles divide an ordered data set into 4 equal groups, and they are marked with Q1, 2 and 3. If we draw a line with the lowest data value to the left and the highest data value to the right, we can mark Q1 2 and 3 at equal distances on the line, with each section being 25%. Q1 is the same as the 25th percentile, Q2 is the same as the 50th percentile and Q3 is the same as the 75th percentile.
There is a fairly simple way to find the data values of a data set that correspond to Q1, Q2, and Q3. Using our data set from earlier, we again first arrange the data in order of smallest to largest. Next, we find the median of the data values, which will be the value of Q2. Since we have an even number of values in the data set, 20, the median will be between the two middle values, value number 10 and value number 11, which are 15 and 16. Add them together and divide by 2 and we get 15.5 as the median, which is Q2.
Next we find the median for the values that fall below Q2, which will be the value of Q1. Since we have an even number of values in this section of the data set, 10, the median will be between the two middle values, value number 5 and value number 6, which are 9 and 10. Again add them together and divide by 2 and we get 9.5 as the value of Q1.
Next we find the median for the values that fall above Q2, which will be the value of Q3. Again, we have an even number of values in this section of the data set, 10, the median will be between the two middle values, value number 15 and value number 16, which are 21 and 23. Add them together and divide by 2 and we get 22, which is the value of Q3.
Another concept that is important in regards to percentiles is the interquartile range or IQR, which is the difference between the third and first quartiles, written as IQR = Q3 minus Q1. So, in our example this would be 22 minus 9.5, which is 12.5 as the interquartile range for the data set.
The interquartile range can be used as one way to identify possible outliers. An outlier is an extremely high or low data value compared with the other data values in the data set and it can have a dramatic effect on the mean and standard deviation of a data set. For a visual reference, here is a dot plot, and you can see all of these values kind of bunched up together, but way over here to the right is this lone value, which just seems to be out of place, and it could possibly be an outlier. Maybe a researcher mistakenly marked this value or read the wrong number.
Using the same data set we have been for this video, I wrote in 170 instead of 17. We are going to use the IQR to identify any possible outliers in this altered data set.
First we arrange the data in order of smallest to largest. Next we go through the process of finding Q1 and Q3, which are 9.5, and 23.5. So, the interquartile range is Q3 minus Q1, which is 14. Next we multiply the IQR by 1.5, which is 21.
Now we are going to subtract that number 21 from Q1, to get -11.5, and then add 21 to Q3, which is 44.5. We have now created a new range of -11.5 to 44.5, and any number outside of that can be considered an outlier according to this method.
The rules for this procedure are that any data value that is smaller than (Q1 - 1.5) times the IQR, or any data value that is larger than (Q1 + 1.5) times the IQR. One note, this is only one of the methods to check for outliers and we will cover other methods in future videos.
Timestamps
0:00 What Are Quartiles?
0:27 How To Find Values For Quartiles
0:38 How To Find The Value For Quartile 2
0:59 How To Find The Value For Quartile 1
1:20 How To Find The Value For Quartile 3
1:43 What Is (IQR) Interquartile Range?
2:06 How To Use IQR To Find Possible Outliers
This is the most satisfactory video in my STAT life. I lack enough words to thank you except say God Bless you. I was not lucky to get this video in high school and I was suffering a lot.
Thank you! Very concise & clear
This is amazing!! Thank you so much!
Thank you! Clear and great explanation
Smooth. So, so smooth. Good one sir.
you deserve more than subscribe and like
'liked'. Thank you for the video
great video !!!
why are you multiplying by 1.5? It was not explained. Somebody please help me too?
I would like to know as well. Did anyone clarify this?
after taking the 1.5 into more consideration, the bell-shape distribution usually has an outliner of 0.15%. To include this in the IQR, it looks like the 0.15% was converted to a whole number by moving the decimal over one spot. Thats my "educated guess"..lol
You're awesome!
Perfect!
Its consice and clear bruh!!
thank you
thank you . great explanation
that's amazing
I was looking for How to calculate IQR online today, after watched several videos and reading solutions, I think the method you used here maybe easy to understand, but the result may also be wrong.
When calculate Q1 and Q3 by , by using formula (n+1)/4 and (n+3)/4, you get 5.25 and 15.75, therefore Q1= 9x0.75+ 10x0.25= 9.25 Q3=21x0.25+23x0.75 =22.5 and the IQR=Q3-Q1=13.25
Kpa 19.4 normal range
Q1 IS 9.25 NOT 9.5
how is q1 9.25?