Definition of Quartiles and How to Find Them

Learn what a quartile is in Statistics, and how to find them.
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I was trying to normalize an array in JavaScript.
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Thank you very much for your explanations, they are very clear and they managed to made me understand how quartiles works. Thanks from France

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I'm glad the video helped. I have a lot of Stats videos, so make sure to check them out.

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[@MathandStatsHelp]

I'm glad it helped. Thanks for subscribing!

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How did you get 13 as the maximum, of the sum when 4.5 and 10.5 equals 15? please let me know.

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May God bless you♥️

[@MathandStatsHelp]

You're welcome. Always like to hear that it's helping someone

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[@MathandStatsHelp]

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[@user-bg6kl1hk6]

@@MathandStatsHelp Execuse Me Mam, Will You please tell me the difference between quantile and quartile?

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Thanks very easy tutorial, short and consice. Thanks, definitely subscribing.

[@p.chandra2444]

Hi, I am a little bit confused about the calculation as I found another way to calculate the quartiles in a book. Please, let me know if the below explanation is correct or not and what is the best way to follow:
Q1 (First quartile) = .25(n+1)
Q3 (Third quartile) = .75(n+1)
According to this method, I get different values for Q1 and Q3 in both of your datasets.

[@MathandStatsHelp]

To me the formulas you have are a more complicated way of doing this. You would get the same answer. To use the formula you have, you would plug in the 14, because I have 14 values in one of the data sets. 0.25(14+1)=3.5 and .75(14+1)=10.5. These aren't the answers to the quartiles, they are which data value would be your quartile. You would still have to put your data in order from smallest to largest. The 3.5th term would be the midpoint between the 3rd and 4th term. The 3rd term is 3 and 4th term is 4, so you would find the midpoint which is 3.5. The 10.5th term would be the midpoint between the 10th and 11th term. The 10th term is 8 and the 11th 9, so the midpoint would be 8.5. Same answer, but more complicated.

[@p.chandra2444]

@@MathandStatsHelp It is super clear now, Thank you. ;)

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Thank you! I needed to know what q4 was because I was confused

[@MathandStatsHelp]

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Sirsly

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[@MathandStatsHelp]

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I happened to be on my app at the moment

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[@m00sing]

Thank you for this. Just a little confused on why we include all points in the first half/2nd half when we have even data points vs. only looking below/above the median in an odd data points scenario.

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[@MathandStatsHelp]

You're welcome

[@patrickrodriguez3607]

Not applicable for Q3 when 3/4(n+1)

[@laylayalexandraysabels.9208]

Do I need to round off the 3.5 if ever I encounter an answer like this in getting the quartiles?
Thanks btw, it's not confusing anymore.

[@MathandStatsHelp]

If you get something like 3.5, just leave it as is. Glad you're not confused anymore.

[@carlosbecerril9126]

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[@eshaanrai2712]

Hey amazing vid but could you please also make an video on inter quartile range. IDK y in my book its given as Q3 - Q1,shouldn't it be q4 - q1 ?

[@MathandStatsHelp]

The interquartile range (IQR) is found by Q3-Q1. It is the range of the middle 50% of the data. It is resistant to outliers, where the range (max-min) is not. This video that I have shows how to create a box and whisker plot. I use the IQR to find outliers. I show how to find the IQR: ruclips.net/video/Kl60eLKix7s/видео.html . Hope it helps.

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[@MathandStatsHelp]

You're welcome

[@megatmuhammadikhwanbinmega8075]

you're an angel.. thank you for your help😁love from Malaysia.. I've question...my data is 7,10,11,12,12,14,15,15,16,23,26...
how to find Q1 and Q3

[@veerakanneboina8086]

But in some cases formulas are used to calculate the term(1st or 2nd), then they are interpolating the values. Which is correct.

[@MathandStatsHelp]

Both are acceptable. It really depends on the software and instructional methods of the textbook.

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Excellent. Very understandable. Many thanks!

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Happy to hear it was understandable!

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[@sanjinatithi5402]

Thanku your video is amazing.can u help me by describing this..
Q1=1st quartile is the value of the variable below which there are 25% of the individual observations.
Q2=2nd or middle quartile is the value of the variable below which there are 50% of the observations
Q3=3rd or upper quartile is the value of the variable below which there are 75% of the observations

[@MathandStatsHelp]

That's correct

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[@MathandStatsHelp]

You're welcome

[@cris-genix9981]

This is good thank you still a little confused on how when add the medians and divide by 2 for 10 plus 12 you got 10.5 but thank you .

[@MathandStatsHelp]

You find the average of the two middle numbers (that's why I divided by two) when you have an even number of data points. If you have an odd number of data points, it's just the middle number.

[@Selvax94]

The explanation is simple and very straightforward. However I'd like to raise a criticism against quartiles: BY DEFINITION they are supposed to break the data pool in 4th, right? So how come they are fuc*ed up? Standing on what their definition says, q1 should be the last 25%, q2 the 25% just above q1, q3 still above q2 and q4 the first 25% of the data. E.g. n = 100 --> q4 = n1 to n25; q3 = n26 to n50; q2 = n51 to n=75; q1 = n=76 to n=100. Why am I so incapable of finding any better historical explanation?

[@MathandStatsHelp]

There are different ways of calculating quartiles. This is the most straightforward way. Approximately, 25% of the data points fall in each quartile. If you have a data set that has a number of terms not divisible by 4, it's not going to be evenly distributed. Your reasoning with the values in each quartile for the 100 points is accurate, we just start with the first quartile as being the first 25 data points or the 25th percentile. You're just finding the point at which those first 25 points end. Q2 is where the next 25 points end or the 50th percentile or the median. Q3 is where the next 25 end of the 75th percentile, and the max is the end of the next quarter of the data or the 100th percentile. In Excel and some other stats software, the quartiles are calculated differently then I showed by actually finding the percentiles. The method I show is used the most frequently in textbooks for small data sets. It is breaking the data up into 4 parts.

[@isaiah352sharon9]

Thanks very much

[@A9Eros]

I have a question, given this data set. 59,79,80,84,88,99,104,107,109,111,112,113,114,119,122,122,127,128,131,131,133,135,139,140,142,142,144,149,152,155,158. What throws me off is that I have an odd number of 31 total numbers. Given that, how would I know what to separate to determine the first and third quartiles? I've been relearning mathematics and this stuff is a bit fuzzy for me. I already know that the median is 122.

[@MathandStatsHelp]

Since the median is the middle number, you just ignore this one for the lower and upper halves. It doesn't go into either. Q1 is the median of the lower half, since there are 15 numbers below the median it would be the 8th term. Q3 would be the 8th number above the median.

[@A9Eros]

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Happy to hear it helped you!

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