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S1 Measures of Dispersion - very simple question about lower + upper quartile watch

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    I just started doing S1 today, but I didn't understand this and it was the end of the lesson, so my teacher couldn't help me and I wasn't able to stay behind after school for help.

    As a general rule, I know that if you have an odd number of pieces of data, you must add 1 in order to make it so you have an even number of pieces of data. If it is already even, you can leave it as it is. Is this correct (for finding quartiles and medians)?

    Here is the question I am talking about:
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    Anyway, I thought that if you have an even number of pieces of data, like this example here with 100 pieces, to find the lower quartile, you just divide the 100 by 4, giving you 100/4=25th piece of data is the lower quartile. This method worked for me in past examples too we did in the lesson.

    However, the mark scheme says that for Q1, when they do it (part b), they then say that because the answer is 25, the average of the 25th and 26th values is Q1, which is 0.5. Why do you take the average of the 25th and 26th values?

    At the bottom of this I have included an image of the question for finding the lower quartile Q1, which I just did 11/4 (11 pieces of data) which gave me 2.75, which rounded up gives the third piece of data, which was 400. That was correct. So why do you need to find the average of the 25th and 26th pieces of data in this instance?
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    I've just watched examsolutions video on this topic: https://www.youtube.com/watch?v=wNamjO-JzUg
    and he does it as simple as I did for the question at the bottom; just make the number of pieces of data,n, an even number, then divide by 4 to find Q1. He doesn't talk about finding an average of the 25th and 26th pieces of data when your answer for Q1 is 25, so why do you need to do that?

    Thanks!
 
 
 
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