S1 Quartiles Watch

Browncoat
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#1
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Hi

Quick question for the S1 exam tomorrow. I had a quick search through previous posts, but was yet to find a definitive answer to my question.

How are we meant to work out quartiles? (Edexcel AS S1)

I had been taught to use:
Q1 = (n+1)/4
Q2 = (n+1)/2
Q3 = 3(n+1)/4

but the answers given by these seem to disagree with exam papers, like, for example, when n=50. My quartile terms are now:
Q1: 12.75th term
Q2: 25.5th term
Q3: 38.25th term

My questions are these:
1. Do I use the rule of thumb: "Use 'n+1' for n<100"
2. Do I round anything that's not a half?
ie using the example above,
Q1 = 12.75th term => Q1 = 13th term
Q3 = 38.25th term => Q3 = 38th term

I had been using interpolation, but this hadn't been giving the correct answers, so should I be rounding instead?

Thanks
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aqfrenzy
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for Q1: 0.25n. If the result is an integer, take the mean of the 0.25n'th and (0.25n+1)'th observation. i.e. if 0.25n=15 then take the mean of the 15th and 16th observation.

If the result is not an integer, take the observation corresponding with the next whole number. i.e. if 0.25n=15.2 take the 16th observation.

This can be applied to Q2 and Q3 replacing 0.25 with 0.5 and 0.75 respectively.
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aqfrenzy
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when n=50, q1 is 13th term, q2 is mean of 25th and 26th term. q3 is 38th term.

but this is when you have every value of the data. when using grouped frequency tables you just put in the exact value into the interpolation formula.
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Prudence Slutsky
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I was taught to use Q1 = n/4, Q2=n+1/2 and Q3=3n/4

For Q1 and Q3, if you don't get an integer, ALWAYS round up.
If you do get an integer, r, then it's 1/2 of r add r+1.

For Q2, if it's not an integer, but lie between r and r+1, then it's 1/2 of r add r+1.
If you do get an integer, take it.

Hope that isn't too confusing
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Browncoat
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Thanks everyone!

That clears stuff up a lot.
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eddieoll
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"For discrete data divide n by 2. When n/2 is a whole number find the mid-point of the corresponding term and the term above. When n/2 is not a whole number, round the number up and pick the corresponding term.
For continuous grouped data divide n by 2 and use interpolation to find the value of the corresponding term."
Edexcel AS and A level Modular Mathematics
Series Director: Kieth Pledger
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OfstedMonster
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Nobody is asking why. Why do we round up. If n=14 then n/4 = 3.5 or (n+1)/4 = 3.75 why do we not try and find the appropriate point between the 3rd and 4th term why do we rely on this rule that we always round up?
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