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Interquartile range of ungrouped data

I've seen different methods in different textbooks for this. I'm wondering how a GCSE student would tackle it and what their answer would be.

Find the interquartile range of this set of data:

1,2,3,5,7,9

What answer would you get? I would think most people will get one of the two answers below:

Spoiler

I'm currently teaching a yr 9 class IGCSE material where finding the IQR of ungrouped data doesn't seem to be in the syllabus. It doesn't really matter which method I teach them, I'm just interested in how it's taught in the UK.

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Reply 1

Math12345

Original post by notnek

Spoiler

InterQuartile Range = Upper Quartile - Lower Quartile
IQR = UQ - LQ
UQ = (3(n+1))/4
LQ = (n+1)/4

n = 6

UQ = (3(6+1))/4 = (3*7)/4 = 21/4 = 5.25th number = 7.5
LQ = (6+1)/4 = 7/4 = 1.75th number = 1.75

IQR = 7.5 - 1.75 = 5.75

I think this is correct. :smile:

Reply 2

Notnek

Original post by Math12345

That seems like a better answer but I've never seen a method given like that in a textbook.

There's usually some form of rounding involved to make things a bit simpler.

Reply 3

TenOfThem

Original post by Math12345

Me too

Reply 4

TenOfThem

Original post by notnek

That seems like a better answer but I've never seen a method given like that in a textbook.

There's usually some form of rounding involved to make things a bit simpler.

imo

unlikely question for GCSE

Reply 5

Notnek

Original post by TenOfThem

Me too

If the position found is a fraction, I've seen most textbooks round to the nearest integer or find the mean of the two numbers whose positions are the floor and ceiling of the number.

Is the method that math12345 gave the standard way it is taught at GCSE?

What about if the position found was something like 1.72?

Reply 6

raheem94

Original post by TenOfThem

Me too

Edexcel S1 don't do this.

I will do it in this way,
UQ = 3n/4 = (3*6)/4 = 18/4=4.5 So UQ is the 5th term: 7
LQ = n/4 = 6/4 = 1.5 So LQ is the 2nd term: 2

IQR= 7-2=5

This is one of the reason i hate stats, methods differ by boards.

Reply 7

Notnek

Original post by raheem94

Thanks for that. So it does vary across boards which is what I expected.

Reply 8

raheem94

Original post by notnek

If the position found is a fraction, I've seen most textbooks round to the nearest integer or find the mean of the two numbers whose positions are the floor and ceiling of the number.

In edexcel S1 they round to the nearest integer, i don't know about GCSE.

Reply 9

TenOfThem

Original post by notnek

I would expect it to be one of the values or midway between 2 values

The method used here is the same method we would use for grouped

Reply 10

raheem94

Original post by notnek

Thanks for that. So it does vary across boards which is what I expected.

I hate S1 a lot due to these reasons, there is no single method to do these questions.

Reply 11

Math12345

I used the method from GCSE Statistics and Maths (Edexcel).

Reply 12

raheem94

Original post by Math12345

I used the method from GCSE Statistics and Maths (Edexcel).

By maths(edexcel), do you mean A-Level edexcel maths S1??

Reply 13

TenOfThem

Original post by raheem94

By maths(edexcel), do you mean A-Level edexcel maths S1??

no, he means GCSE

Reply 14

Math12345

Original post by raheem94

By maths(edexcel), do you mean A-Level edexcel maths S1??

No - GCSE Mathematics and GCSE Statistics. Both are the Edexcel board.

Reply 15

raheem94

Original post by TenOfThem

no, he means GCSE

Original post by Math12345

No - GCSE Mathematics and GCSE Statistics. Both are the Edexcel board.

GCSE methods may be different.

In the edexcel A-Level S1 book they have written this:

Reply 16

TenOfThem

Original post by raheem94

GCSE methods may be different.

In the edexcel A-Level S1 book they have written this:

Stats is all about indication and interpretation

5.5, 5.75, 6

they are not different enough to matter in the context of IQR

TBH IQR is not a relevant calculation for 6 pieces of data

Reply 17

raheem94

Original post by TenOfThem

Stats is all about indication and interpretation

5.5, 5.75, 6

they are not different enough to matter in the context of IQR

TBH IQR is not a relevant calculation for 6 pieces of data

Tbh i just want to get fine marks in my S1 and S2 exam, i am not very interested in learning different techniques and increase my stats knowledge.

I hate it from all angles!

Reply 18

TenOfThem

Original post by raheem94

Tbh i just want to get fine marks in my S1 and S2 exam, i am not very interested in learning different techniques and increase my stats knowledge.

I hate it from all angles!

So why worry

You have your method ... that will get you marks ... use it

Reply 19

raheem94

Original post by TenOfThem

So why worry

You have your method ... that will get you marks ... use it

I am not worrying about it, i am preparing for physics which is on Thursday, S1 is on Friday so i will prepare for it on Thursday. Hopefully an easy probability question will come up :smile:

Though one thing has got me worrying, someone today said that the best way to prepare was to learn all the mark schemes, i am not doing this, i will just attempt 1 past paper and just see the answers from the mark scheme, will i get good marks? :biggrin: