Measures of Variation (range and interquartile range)

✅CHECK YOUR ANSWERS✅
ON YOUR OWN ANSWERS
1) Range = 41 years old. The ages of people in line for a roller coaster vary by NO MORE than 41 years.
2a) Interquartile range (IQR) = 38 pages. The middle half of the data varies by NO MORE than 38 pages.
2b) 468 pages is an outlier because when you check using the IQR, 468 is greater than 455. (398 + 1.5(38) = 455)
This video introduces measures of variation, including the range and interquartile range. We discuss how to calculate both of those measures and what they tell us about the variation of the data. The helps us understand if there are any outliers and also how spread out or close together our data is.

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Maybe a dumb question but where does the 1.5 come from? Is this a standard number or did you calculate it from the data given?

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Thanks this video was helpful for me at first I saw this name quartile or interquartile I was afraid of that but after watching this I felt confident sir. Thanks alot.

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But how do i get quatiles when the data is so many?? i need the law in exams right??

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Thanks for the help. Could you also post the answers to the questions you provide for solving? It would be better if we could cross-check our answers. Cheers :)

[@AnywhereMath]

Good idea. I'll work on putting them in the description.

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5:07 a shorter from for 1st quartile is Q1

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[@mcpasierb62]

I can't find an explanation to why we use the term quartile then only use Qi and Q3...you spoke of Q2 being the median but what happened to Q4 ? Maybe I'm taking the term quartile too literally???

[@AnywhereMath]

+Marie-Catherine Pasierb I suppose Q4 would include the entire data set.

[@ashgene]

when you cut a line (of data) at 3 places (Q1,Q2,Q3) you get 4 line segments(data groups) each is 25% and called a quartile

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Can I ask a question Is it truth that if the range is high the numbers are close together?

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[@andresg253]

Where did u get the 1.5 from ?? For the outliers!

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Its just a rule that goes with finding outliers. I was confused about it until my teacher told me why

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[@kayl713]

I apologize in advance if this questions had already been asked, but.... when would it ever be useful to find the IQR? Is there an example of how this information would be useful in data presentation?

[@AnywhereMath]

That's a great question. IQR will tell you whether or not the middle 50% of your data is really close together or spread out. For example, if you sold shoes and found that after collecting data on the shoe sizes sold your IQR was 2 (e.g. half of the data could be from size 6 to 8), that would mean that most of the shoes you sold are similar sizes. If the IQR was 6 (e.g. half of the data could be from size 4 to 10) then you know that you're selling a large variety of sizes.

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Where can I check my answers?

[@greatethingstakegreattime5263]

Here's the Answer A: median :382 Q1=360 Q2=398 IQR=38 B: the lower quartile has no outlier While the upper quartile has outlier Here's the Formula for B Q1-1.5(IQR) 360-1.5*38 360-57= 303 And the lowest number in the lower half is 350 so theirs no outlier Second upper half Q3+1.5*38= 398+57=455 the highest number in the upper half is 468 so there's outlier

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[@greatethingstakegreattime5263]

Here's the Answer A: median :382 Q1=360 Q2=398 IQR=38 B: the lower quartile has no outlier While the upper quartile has outlier Here's the Formula for B Q1-1.5(IQR) 360-1.5*38 360-57= 303 And the lowest number in the lower half is 350 so theirs no outlier Second upper half Q3+1.5*38= 398+57=455 the highest number in the upper half is 468 so there's outlier

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0:04

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[@renenavarro2889]

How did you get 30 from the 4th example?

[@AnywhereMath]

+Rene Navarro 1.5 times 20 equals 30. When you write it like 1.5(20) the parentheses mean multiplication

[@oscarmu901]

So is there an outlier on the upper half of question 2) it goes lower than 363.5?

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why did you chose 1.5???

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It would be more helpful if when you give the viewers an problem to solve if you came back with the answer so they know if they got it correct or not.

[@AnywhereMath]

The answers to the "On Your Own" questions are in the description below.

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hey? whats your answer for the outliers?

[@biyolazaro6046]

Outlier 1.5(23) Q1-1.5(IQR)= 322.5 Q3+1.5(IQR)=432.5 Is this correct?

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where is the 4th quartile? theres only 3 in example 2. (sorry, i need this for my biostat)

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Chez Doge the formula is Q3-Q1 ➗ by 2

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so the 6 and 7 number will always be the meadian? what if there is only one in the middle and not two

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what?

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what if its odd number you only did even

[@miss_sxturn1220]

9:22 I don't get this part... ;^;

[@mintygamerA]

Well, first you find the IQR, then you subtract 1.5(IQR) from the first quartile. If there is a number less than what you got from the equation, thats an outlier. do the same for the 3 quartile,adding not subtracting, but if there is a number greater than what you get from the equation, that will be an outlier. Hope this helps!

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Great! Happy to help :)