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Math Help - Hard Statisitics question

  1. #1
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    Exclamation Hard Statisitics question

    Hi can some help me with this question as i don't understand it at all, and just do not know were to begin.
    Attached Thumbnails Attached Thumbnails Hard Statisitics question-untitled.jpg  
    Last edited by nerdo; January 20th 2009 at 11:03 AM.
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  2. #2
    Member Last_Singularity's Avatar
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    Quote Originally Posted by nerdo View Post
    Hi can some help me with this question as i don't understand it at all, and just do not know were to begin.

    Hard Statisitics question-untitled.jpg
    I can get you started.

    Part A:
    There are a lot choices. Simply pick a measurement in units of customary and metric. Example: pounds vs. kilograms, miles vs. kilometers, Fahrenheit vs. Celsius, etc.

    For instance, take a temperature conversion. We know that the relationship between F and C is: F = 9/5 C + 32.

    So if y_i represented Fahrenheit and x_i represented Celsius, then a is 9/5 and b is 32.

    Part B:
    (i)
    \bar{y} = \frac{1}{n} \sum_{i=1}^{n} y_i = \frac{1}{n} \sum_{i=1}^{n} (a x_i + b) = \frac{a}{n} \sum_{i=1}^{n} x_i + \frac{1}{n} \sum_{i=1}^{n} b = a \bar{x_i} + b

    So the claim is true, as proven by algebra above.

    (ii)
    For \bar{z}, the claim is false. It is up to you to find a counterexample. Pick any arbitrary set of values for x_i and see whether or not \bar{z} = \frac{1}{n} \sum_{i=1}^{n} \frac{c}{x_i} is equal to \frac{c}{\bar{x}}. Most likely not, if you picked your values strategically.

    (iii)
    Since the relationship between y_i,x_i is linear (and thus bijective), the ordering of the values of x_i are preserved during a mapping to y_i. Thus, the smallest value of x_i gets sent to the smallest value of y_i. Same with the largest value and the median, etc.

    (iv)
    Again, find a counterexample.
    Last edited by Last_Singularity; January 17th 2009 at 03:24 PM.
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