Finding Quartiles and the Interquartile Range of Data | Statistics, IQR

How do we find the quartiles and the interquartile range of a set of data? We'll be going over that with an example in today's statistics video lesson! #Statistics #APStats

Finding the first quartile, second quartile, and third quartile of a data set is easy, but it can be time consuming. First, we have to order our data from least to greatest, then we can find the median of the data - the middle value - which is the second quartile, often written as Q2. Then we just find the median of all the data below Q2, which gives us Q1. Then we find the median of all the data above Q2, which gives us Q3. We have then split the data into four parts: the data less than Q1, the data between Q1 and Q2, data between Q2 and Q3, and data above Q3.

We can subtract Q1 from Q3 to find the "interquartile range". So Q3 - Q1 equals the interquartile range or IQR. This is a measure of how spread out the data is around the middle. If the interquartile range is very large then the middle 50% of the data is very spread out.

SOLUTION TO PRACTICE PROBLEM:

First we sort the salaries from least to greatest, giving us this list:

28,000 ; 33,000 ; 42,000 ; 54,000 ; 54,000; 64,500 ; 68,500 ; 69,000 ; 72,000 ; 120,000

Then, the median is the average of the middle two values, the average of 54,000 and 64,500 which is (54,000 + 64,500) / 2 = 59,250. This is Q2.

Then, 28,000 ; 33,000 ; 42,000 ; 54,000 ; 54,000 is the list of data below Q2 - the lower half of data. The median of this data is 42,000 - thus Q1 is 42,000.

Finally, 64,500 ; 68,500 ; 69,000 ; 72,000 ; 120,000 is the list of data above Q2 - the upper half of data. The median of this data is 69,000 - thus Q3 is 69,000.

Lastly, the interquartile range is Q3 - Q1 = 69,000 - 42,000 = 27,000.

I hope you find this video helpful, and be sure to ask any questions down in the comments!

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The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work.

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+WRATH OF MATH+

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[gaby]

this was explained much more easier than my actual teacher thanks

[missme]

Thank you for simplifying this and making it easy to understand

[piztolice]

It's a rare occurrence to find a math video that's not too long but covers what's mentioned in the title with an understandable pace of talking.

[glorysunday]

Thank you for simplifying this for me.
From my calculation I got this; Q1=37, 500
Q2=59, 250
Q3=70, 500
IQR= Q3-Q1
= 70, 500-37, 500

[CakeAndPi]

Awesome! The practice problem was helpful!

[traceylammert]

If the data set is 31, 33, 38, 40, 40, 45, 49, 52, 56, 57, 61, 65 the median would be 47. Is Q1 39? (finding the average using only one of the 40s?) Thanks

[yaretzi]

as a 6th grader i understand this so well thank you so much!

[studyingwhileinyourprime]

This is really interesting the way you simplified it, I am actually studying from prison without face-to-face classes, how will I interact with you for instant responses.

[arandomguy]

testing out in 6 days and the school site is down so i have to use this,

[arinday]

who else is hefre from kevi bros its arin