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October 24th, 2015, 12:13 PM   #1
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Should I use interpolation or approximation here?

I am a S1 maths (Edexcel) AS student in the UK. My question: Say we have a stem-and-leaf diagram with 26 values. We want to find the lower quartile. To get the marks for our specification, we need to find the [(n+1)/2]th value. This is the 6.75th value.

So I use interpolation to find the said value:

6th value + (0.75*difference between 7th and 6th values)=value of the lower quartile.

But my S1 textbook says you should round 6.75 to 7 and just give the 7th value as the answer.

So: Should I use interpolation or approximation?????

Thanks!
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October 25th, 2015, 02:54 AM   #2
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Interpolation that involves 1/4 or 3/4 is usually regarded as "too complicated" (although some authors use it).

In the following definitions, m is the number of values and is at least 2, n is the integer part of m/4, and the values are prearranged in non-descending order.

If m = 4n or m = 4n+1, the first and third quartiles are usually defined as the (n + 1/2)th value and the (m - n + 1/2)th value respectively.

If m = 4n+2 or m = 4n+3, the first and third quartiles are usually defined as the (n + 1)th value and the (m - n)th value respectively.

In all four of the above cases, there are n values that precede the first quartile and n values that are preceded by the third quartile.
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