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MEI S1 Question

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    I've been trying to do this question, and I'm unsure of whether I'm doing the right thing or not! Any help would be much appreciated

    In fact, the exact values of the mean and standard deviation of the number of
    chapters per book are 14.7 and 6.1. Use these exact values for the remainder of the question. (Before this there was a grouped frequency table)
    The number of pages, p, in a book is modelled by
    p=20x+15
    where x is the number of chapters in the book.
    Calculate the mean and standard deviation of the number of pages as given by this model.
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    (Original post by XmayaX)
    I've been trying to do this question, and I'm unsure of whether I'm doing the right thing or not! Any help would be much appreciated

    In fact, the exact values of the mean and standard deviation of the number of
    chapters per book are 14.7 and 6.1. Use these exact values for the remainder of the question. (Before this there was a grouped frequency table)
    The number of pages, p, in a book is modelled by
    p=20x+15
    where x is the number of chapters in the book.
    Calculate the mean and standard deviation of the number of pages as given by this model.
    What did you try?

    Hint:
    Spoiler:
    Show
    What is E(aX+B) and Var(aX+b) in terms of E(X), the mean, and Var(X), the variance, if you've come across it in that form?
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    (Original post by SeanFM)
    What did you try?

    Hint:
    Spoiler:
    Show
    What is E(aX+B) and Var(aX+b) in terms of E(X), the mean, and Var(X), the variance, if you've come across it in that form?
    I haven't come across this yet
    The questions said earlier the total number of books is 60
    So using the mean I figured there's 882 chapters in total but I don't know where to go from there


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    My friend suggested simply substituting in the mean number of chapters per book into the question but I feel that's far too simple!
    Thanks for replying btw 😊😊


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    (Original post by XmayaX)
    I haven't come across this yet
    The questions said earlier the total number of books is 60
    So using the mean I figured there's 882 chapters in total but I don't know where to go from there


    Posted from TSR Mobile
    Ah okay, it's a different area of the syllabus rather than relying on questions from a previous part, though that is always a good spot - sometimes questions are directly link, others indirectly.

    Basically you use the properties in the previous post, you should look for it in the textbook first before attempting it.. but to give you an idea,

    if on average a book has 14.7 chapters, and the number of pages is modelled by 20x + 15, then using the same 'average' as the value of x, you get on average (20*14.7) + 15 pages per book. that's how you make sense of it but more formally, if you have the mean written as E(X) (in this case it is x) then E(aX+b) where aX + b is a function (in this case it is 20x + 15) E(aX + b) = aE(X) + b, and then you use E(X), a and b to work that out.

    Var(aX+b) is a^2 Var(X). So with the mean, if you multiply it and add something they both affect the new mean, but if you add something to a set with a fixed variance it doesn't affect it at all. Don't worry if that doesn't make sense yet, should do after you learn it.

    Check out this video

    https://www.youtube.com/watch?v=R92_aakUZUc
    skip to the bit about linear expectation (aX+b) if you want.
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    (Original post by SeanFM)
    Ah okay, it's a different area of the syllabus rather than relying on questions from a previous part, though that is always a good spot - sometimes questions are directly link, others indirectly.

    Basically you use the properties in the previous post, you should look for it in the textbook first before attempting it.. but to give you an idea,

    if on average a book has 14.7 chapters, and the number of pages is modelled by 20x + 15, then using the same 'average' as the value of x, you get on average (20*14.7) + 15 pages per book. that's how you make sense of it but more formally, if you have the mean written as E(X) (in this case it is x) then E(aX+b) where aX + b is a function (in this case it is 20x + 15) E(aX + b) = aE(X) + b, and then you use E(X), a and b to work that out.

    Var(aX+b) is a^2 Var(X). So with the mean, if you multiply it and add something they both affect the new mean, but if you add something to a set with a fixed variance it doesn't affect it at all. Don't worry if that doesn't make sense yet, should do after you learn it.

    Check out this video

    https://www.youtube.com/watch?v=R92_aakUZUc
    skip to the bit about linear expectation (aX+b) if you want.
    Thank you so much! I'll check out the video too 😊


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