Estimating median, quartiles, percentiles from a grouped frequency table : ExamSolutions

Median, quartiles, percentiles from a grouped frequency table. Estimating values for the median and quartiles for grouped data than ungrouped data.
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[@MrGhostBoy77]

Video came out 8 years ago and still the best video on KZbin

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and this comment is one year ago haha

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@@seleira7157 and this reply is one year ago lol

[@starslainer9093]

@@comixsuper5665 THIS ONE is 1 month agoXD

[@sunmeetkhurana669]

I was panicking for 12 minutes ago because my S1 mock is tomorrow and I had no clue about interpolation, but thanks to you I have understood it!! Thank you so much!!

[@ExamSolutions_Maths]

+Sunmeet Khurana Good. Hope it goes well for you tomorrow

[@alleniverson9760]

History repeats itself

[@yeetspageet5679]

+Allen Iverson always does

[@bob1city112]

has just repeated itself this year aswell stats mock tomoz ;)

[@user-pf7jv8sv8w]

ARproductive bruh you aren’t prepared it seems ;)

[@ExamSolutions_Maths]

The median would be in the (20+1)/2 position if the data were discrete. In other words the 10.5th value which will then be the mean of the 10th and 11th values.

[@slow2199]

🎉

[@AsiansCrazy]

you are an absolute legend...stay blessed...god bless you sir!

[@prodxtendo]

The plain old method that teachers teach aren't any good without proper understanding of it. Thank you for what you do.

[@ExamSolutions_Maths]

You're very welcome!

[@muneungBeing]

This channel is always helped my mathematics works :)

[@ExamSolutions_Maths]

Pleased to know you have now got it. Well done.

[@sonalchaudhary6957]

I am so impressed, so well explained

[@noonecares6816]

i love your vidoes becuase you explain every step you'r going through unlike other people skip it through

[@nocallerid1514]

Greatest maths video I’ve watched

[@Andrew6James]

Hi, Do we only use interpolation when estimating means and quartiles in grouped frequency tables? If the question asks to find the mean and quartiles as in videos 2 & 4 in S1 do we simply use (n+1/2)? Thanks

[@willsaldana998]

Your a legend thanks so much for your videos helped me so much

[@gaz706]

Thank you so much for uploading this video. Excellent and so easily explained... 👏

[@ExamSolutions_Maths]

Appreciated.

[@piedpiper7384]

wow you made it so easy to understand! Thanks

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Wings are made to fly ARMY!! 😂😂😂

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the KZbin algorithm is really shit. Have to work hard to get a golden video like this.

[@ExamSolutions_Maths]

@Peacock2613 Do you realise that these are free videos done in my own time and you want to complain. Shame on you.

[@mohammadmunzurulhaque3197]

Smiled for the first time finding the median, that was dead helpful Sir :D

[@phoenixreed4012]

this was so sososo useful thank you!!

[@ExamSolutions_Maths]

Because the class limits and class boundaries for this example are the same. If it were 10-19, 20-24, I would use 9.5 - 19.5 etc.

[@wendelladrian03]

Thanks sir! Much easier than the method used by my teacher. :)

[@lucasmunozazevedo5104]

best explanation i have ever seen

[@karedad07]

Finally understood this completely.

[@chookypoo77]

SO useful Thank you!!!!!!

[@denisbrosnan2008]

Great explanation. Thanks

[@analedlastoverlover8217]

this was greeeat! thank u so much

[@dylan432]

Hi good sir, are all your videos still relevant to the most recent specification? They’re extremely helpful

[@dgc312]

hi, im finding it very difficult getting my head around and understanding the theory/steps to find out the quartile/percentile (06:10 - 07:45) , could you please share the formula used that explains what figures i should be using in that calculation please i just cant seem to understand the formula you are using? is there a layman's formula i can refer to? thank you

[@aravindmani304]

Thank you so, so much, ExamSolutions. I missed the lesson in class on this, and I was very confused on it. This cleared everything up. I will be sure to like, subscribe, and check out your other videos!

[@jamesalster4304]

Will u reply 6 years later?

[@hellraiserinsane]

Thanks a lot man.keep it up

[@deepakbalaji8755]

Sir u r a LEGEND.........

[@riesheenacordero230]

Made so much sense, it is very clear. Thank you so much!

[@ExamSolutions_Maths]

+Riesheena Cordero Good to hear. Well done.

[@cjhook1]

In your previous video on Cumulative Frequency Curves, you stated that for example 165-175 mean't 165< h ≤ 175 but here you're saying in your example 10-20 means "we have four values which are greater or equal to ten but less than 20" which looks like this, 10 ≤ f < 20. Why has the ≤ sign swapped around?

[@jwa610]

thanx 4 the video.so helpful

[@Taiyella]

Yay thank you!

[@peteer4049]

So how can I use this method of Interpolation to work out deciles and also the inter-quartile range from a grouped frequency table?

[@Allyamjad]

Video up 10 years ago and here it is, saving my ass from failure

[@personager]

I see. Just one more question; when asked to find the median of a small set of discrete data (say 20 pieces of data represented on a stem and leaf diagram), I use the (n+1)/2 formula and get the 18.75th term as the answer. Would I round it down to 18.5 and therefore find the mean of the 18th and 19th terms to obtain the answer?

[@madanpal2370]

yes. this will help me alot

[@hadijaffri9856]

Anyone ever told u that u are a living legend?

[@mindfulawareness1]

Love this. Please explain how the 'comparing the intervals equation' works. Why does the lhs equal the rhs?

[@mindfulawareness1]

...also my first intuitive attempt gave me 42. P80 relative to the whole, not just to the interval: lb10 and ub50. lf0 and uf20 gives 42. Why do you apply P80 to the interval alone, not across the whole ?

[@dgc312]

ok thanks, could you share this formula please, as if i see it from a different perspective i may start understanding it. what are your views on this method of finding out the quartile/percentile by just using the graph rather than a formula/calculation? do they both bring the same answer?

[@ExamSolutions_Maths]

@MassiusClay7 No probs. Thanks for your support.

[@sushiismyfavorite]

helped so much, thanks! :)

[@ExamSolutions_Maths]

sushiismyfavorite Thanks for looking at it. Hope my other videos help to.

[@ExamSolutions_Maths]

Hope you find the rest useful

[@ibrarelsherif]

Hi Sir, I would just like to know how you obtained the value 6 when finding out Q2 (Median)?? Kind Regards

[@srinivasanmridhula5131]

Awesome!

[@johnbutkis2544]

Can I just ask when do you use the bounds when calculating the median, when the question says to the nearest measurement or when there are gaps?

[@MrsEileenDover]

what do we do for the upper and lower boundaries when the class width is 0-1?

[@mokalokasoka5163]

Thank you ❤❤

[@mariehill6547]

Thx!

[@kisakiyiikapearl]

thank you :)

[@ExamSolutions_Maths]

@naruto2710 10- would mean greater than or equal to 10 but less than 20. So the mid point would be taken as 15

[@personager]

Here you used the formula n/2 to find the median because, as you said, that data given is continuous (i.e. 10-20, 20-25 etc.). But what if the data given had gaps in it and therefore not continuous (i.e. 10-20, 21-25 etc.)? Would you then use the formula (n+1)/2?

[@cardboardlife]

So why is it different in one of your other videos where its greater than the lower bound but = or less than the upperbound? Thanks for the videos very much appreciated. 3rd time doing S1 :/

[@aerhansrirangan6835]

i understand everything but how to do this for grouped data with gaps like 0 - 9 or 10 - 19

[@ExamSolutions_Maths]

Thanks

[@charlesringrose]

What if I was interpolating from a grouped frequency table and the first class is 0-4, the next is 5-9 etc. and I wanted, say, Q1, which was in the first class interval. I know normally you extend the boundaries of the class but how would I approach the zero? Would I make the class -0.5

[@ExamSolutions_Maths]

I would argue that it is dependent on the type of data. If it were the lengths of objects then I would argue it is 0. If it were arrival times then I would argue that it could be -0.5 (being early) 0 being on time and other positive times being late say.

[@alexlewandowski6664]

What is a class boundary?

[@personager]

Or is it that when we make the lower class boundaries for the the non-continuous pieces of data into 9.5-20.5, 20.5-25.5 etc. we convert them into continuous data and therefore always use the formula n/2 when finding medians for grouped frequency data.

[@eviebee4]

thanks a lot :)

[@reese3456]

I'm using the formula Lower Boundary+(Place in group/group frequency X class width), The formula works to obtain the Median however It's not getting the right value for the 80th percentile can anyone explain why??

[@teacherchristtoefur8833]

if the frequency is 20, shouldnt the median be 10.5? edit: sorry im mixing up which number is which edit 2: if the frequency is 20, which is an even number, shouldnt the median be the 10.5th value?

[@MrDeznMark]

Do we have to use the line diagram? Is it Ok to just memorize the general formula instead? Are there any specific instances where the diagram is needed?

[@ExamSolutions_Maths]

You can use the formula if you wish. It is upo to you. I just find the diagram easier.

[@patriciapreye2612]

What if they're 2 classes. How do you determine the median class

[@mystmuffin3600]

what a video!

[@pointeskatecybunny]

Does this mean (having watched the video and read through the comments) that if the class widths do not overlap at all, e.g 10-19, 20-25, the Lower Bound is the bottom number of the class width minus 0.5, and the Upper Bound, is the top number add 0.5 ? (thus increasing the class width by 1)

[@ExamSolutions_Maths]

Yes

[@Triarchie]

ExamSolutions And this would only apply if the data is continuous??

[@ExamSolutions_Maths]

Tririchie Yes

[@584emad]

there was a formula Lower boundary + (n/2 - F)/f * class width ? shouldn't we use this ?

[@semerezeray5776]

i don't need a maths teacher when i have this legend.

[@Cyno7]

i'm confused about finding the midpoint if there is only one boundary for each class. so in your example if it were 10- , 20- , 30- , plz help

[@ExamSolutions_Maths]

Which video?

[@ExamSolutions_Maths]

Exactly.

[@wojciechkostrzewa19]

Thank you sir

[@ExamSolutions_Maths]

No problem, thanks for supporting this work

[@abdimaxamed6285]

sir l need to ask one question and the question is x : 8 9 10 11 12 13 fr: 2 4 8 10 5 3 find a) median b) quartiles ?

[@HaveFun321e]

wouldn't the median be 10.5?

[@hannah918273645]

+Lea Marks 20/2=10

[@TheElectrozoid]

this is continuous data so the formula is N/2 if this was a discrete data then it would be (n+1)/2

[@thesurgeon6473]

TheElectrozoid That's exactly what I needed to know, thank you so much

[@TheElectrozoid]

No problem, i was looking for the answer as well, ExamSolutions answered the same question somewhere below. Good luck fro S1 tomorrow!

[@kylezinho_]

@TheElectrozoid thanks mate

[@ExamSolutions_Maths]

@Lukawa345 Take midpoints of the classes as your x value and then use the necessary formula. Too hard to write out here.

[@ExamSolutions_Maths]

@xoxrandomgirlxoxlol For continuous data we don't tend to add 1 for discrete data then add 1 and divide by 2 to get the position of the middle value.

[@Lukawa345]

How would you then estimate standard deviation?

[@stevedl3150]

How is it that we can see that the 10th value lies in the interval 20 to 25 ? Is it because, in the cumulative frequency column, 10 lies between 4 and 12 ? I`m struggling with this. Statistics was never my strong point. But I`m determined to `get it.`

[@ExamSolutions_Maths]

Yes.

[@barney5189]

I need an answer for the same question asked by Steve DL

[@mahmoudm451]

you should look at the frequency column and not on the cummulative frequency one. consider that (10-20) is "x" and (20-25) is "y" so as (10-20) has a frequency of 4 and (20-25) has a frequency of 8 so together if you see them it will look like x,x,x,x,y,y,y,y,y,y,y,y.......etc for the other values. so clearly a "y" is in the 10th position which is (20-25). hope you got it.

[@fly869]

Steve DL l

[@robinbayser3079]

why do u use the class limits and not the class boundaries?

[@personager]

Or would I round the 18.75th term up to the 19th term (and hence, if I got the answer as the 18.25th term, round it down to the 18th term)?

[@ExamSolutions_Maths]

@OnyxFreq OCR has not

[@mohammadalfatehkhalil6235]

I thought the cumulative frequency n=20 which is an EVEN value. So the median would be the average of 10th and 11th observation. Therefore the average should be 10.5, however, you have used 11, please explain.

[@spiralsausage]

Mohammad Alfateh Khalil Continuous data uses n/2 and discrete data uses (n+1)/2, I believe

[@mohammadalfatehkhalil6235]

Many thanks, I later found it but I appreciate your reply

[@spiralsausage]

Mohammad Alfateh Khalil Actually I'm now thinking that a more accurate description would have been that grouped data uses n/2 and ungrouped uses (n+1)/2 (for the edexcel exam board, not necessary in other boards or situations). I've done a few questions in the new stats and mechanics year 1/as book and that's how they seem to do it.

[@priya200328]

So are median, quartiles, percentiles all the same?

[@amied7361]

i have a question the 4 values are LESS than 20 so when you are doing the number line, shouldn't it be 19 above the 4??? or 5 below the 20? Please reply.

[@ExamSolutions_Maths]

+Amie D I could use 19.99999999999... but 20 is more practical.

[@amied7361]

+ExamSolutions Okay thanks a lot. :)

[@ExamSolutions_Maths]

It is linear interpolation

[@4EVAORLANDO]

if the median was in the 10-20 group what would the numbers on the bottom be?

[@jamestherat97]

For the interval of 20-25 in the interpolation, shouldn't you have used 19.5 and 25.5 as the upper and lower bounds of the interval, not 20 and 25?

[@ExamSolutions_Maths]

jamestherat97 No. There are no gaps between the classes 10-20 means 10

[@dontknow6775]

in percentile how is it 0.8*20 ...i couldnt get it ....can someone help me pleaseee

[@andrewvest7540]

Isn't it wrong that those groups are overlapping? E.g 20 is in 2 groupings?

[@ExamSolutions_Maths]

10-4=6 then multiplied both sides by this value.

[@_phxlo_]

at 5:25, how did you find that the 10th value is between 20 and 25?

[@Ayasir-lo3ir]

watch the video carefully ur not focusing

[@dedly13]

@ExamSolutions there are a huge number of videos on this, i believe the khan academy did a good one

[@littledreams77]

please someone help, why do you not add one when dividing 20 by 2 to find the median (for eg)? because when the data is not grouped you always add one? right? thanks

[@ExamSolutions_Maths]

this is continuous data so the formula is N/2 if this was a discrete data then it would be (n+1)/2

[@littledreams77]

+ExamSolutions thank you! do u know it's continuous data because there are no gaps? ie if there were gaps it would be discrete and you'd add 1 to n

[@ExamSolutions_Maths]

That is correct.

[@ExamSolutions_Maths]

All I am using is a ratio formula. Comparing like with like in the way of intervals. There is a formula but I have always found it far easier to teach this method. Obviously not what you want to hear though, sorry.

[@salmaumma792]

Omgmmgmg thank you so much

[@ExamSolutions_Maths]

No problem - thanks for watching

[@hellraiserinsane]

How is the 10th value.in the interval 20 -25

[@Cyno7]

also because the class widths were irregular shouldn't we have found the frequency density

[@angelstarfire]

Thank you sir!!(>~< )

[@julieannaraza3240]

d7=25+(27-25)(0.3) where did 0.3 came from? it is interpolation of decile

[@antoniaclarke5053]

How and where did you get 0.5 from - e.g (0.5*20)

[@shuzkay]

percentile youre finding times the data you're solving

[@shuzkay]

just add the f and you'll get youre data