In this video you will learn how to find Q1 ( Lower Quartile), Q3
( Upper Quartile) and Interquartile Range ( IQR)
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In this video I would like to talk about finding the Q1, Q3, and IQR, Interquartile Range, this video will be helpful when setting up a box plot or a box and whisker and you may be confused finding these values.
CALCULATING THE Q1, Q3 AND IQR
Step #1: Order the numbers from LEAST to GREATEST
Step #2: Indentify the EXTREMES
Step #3: Find the MEDIAN of the data set
Step #4: Find Q3 or the UPPER QUARTILE (this is the MEDIAN of the
UPPER HALF of the data). You will only use the data to the
right of the original median for this step.
Step #5: Find Q1 or the LOWER QUARTILE (this is the MEDIAN of
the LOWER HALF of the data). You will only use the data to
the left of the original median for this step.
Step #6: Calculate the INTERQUARTILE RANGE by subtracting the
LOWER QUARTILE from the UPPER QUARTILE.
Lets go ahead and look at the first data set.
19 25 16 20 34 7 31 12 22 29 and 16
Step 1 is to order them from least to greatest.
To save time I have gone ahead and done that.
We start at 7 and end at 34
Now we will identify the extremes
The extremes would be 7 and 34
Next you need to find the median of the entire data set
Normally I cross them off, but I will put a mark
I will continue placing marks until I get the median of 20
20 is the median of the data set
Now, step 3 is to find Q3 please notice, since we have an odd number 1 2 3 4 5 6 7 8 9 10 11 we will not include the median in the upper quartile.
I will place a bracket over top of the numbers, and that is our Q3
Next we find the median of the top set.
I will cross out numbers and I find the median to be 29
Now for Q1 I will repeat the same process.
Q1 is the lower quartile and I will mark them off.
16 is the median of the lower quartile
Now for the IQR I take the median of Q3 and subtract that from the median of Q1
29-16 = 13 and the range of these numbers is 34 - 7 = 27
Lets answer these questions
What are the extremes 7 and 34
What is the median? 20
What is Q3? 29
The Q1 is the lower which is 16
The IQR is 29 -16 which equals 13
Lets work one more set to see if we get a handle.
I went ahead a placed these numbers in increasing order
The extremes are 65 and 100
The median of the data set
I will cross these off
You will notice I have two numbers 80 and 82 so the average of 80 and 82 is 81.5
That is the average of 80 and 82
Now since we do not have an odd number we will include 80 and 82 in the set
I will put a bracket around Q1 and around Q3
What is the median?
Q3 is the median of the top set which is 90
Q1 is the median of the lower set and that is 70
The IQR ( interquartile range) is 90 - 70 = 20
Hope that helps you in finding Q1,Q3, and the IQR interquartile range.
Thanks for watching, MooMooMath uploads a new Math video everyday.
For more middle school videos see..
calculating interquartile | find interquartile | math interquartile | Definition interquartile |
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Tagged under: statistics,q1,q3,iqr, quartile,upper quartile,interquartile range,middle school math,6th grade math,box plot,box whisker plot,calculating interquartile,find interquartile,math interquartile,Definition interquartile
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