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Math Help - Standard deviation formula on these question

  1. #1
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    Question Standard deviation formula on these question

    Hi, im not sure if this topic goes in here or not. but it would be helpful if anyone can help me on this, as i got them wrong.
    any formula to use?

    If it is assumed that the marks in Question 3 represent the entire population of marks in which we are interested, what is the standard deviation of these marks?
    A. 10.40
    B. 11.12
    C. 98.19
    D. 113.64
    E. None of the above.

    6. The manager of a restaurant has carried out a small-scale survey to find out how far customers travel to the restaurant. The results for a randomly selected sample of 8 customers were as follows (distances in miles):

    12, 23, 14, 27, 14, 8, 19, 27

    Estimate the standard deviation of the distances travelled by all customers of this restaurant.
    A. 50.86 miles
    B. 7.13 miles
    C. 44.5 miles
    D. 6.67 miles
    E. None of the above.
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  2. #2
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    Quote Originally Posted by chungkayan View Post
    Hi, im not sure if this topic goes in here or not. but it would be helpful if anyone can help me on this, as i got them wrong.
    any formula to use?

    If it is assumed that the marks in Question 3 represent the entire population of marks in which we are interested, what is the standard deviation of these marks?
    A. 10.40
    B. 11.12
    C. 98.19
    D. 113.64
    E. None of the above.

    Mr F says: Do the calculation by applying the formula you have been taught. Where are you stuck?

    6. The manager of a restaurant has carried out a small-scale survey to find out how far customers travel to the restaurant. The results for a randomly selected sample of 8 customers were as follows (distances in miles):

    12, 23, 14, 27, 14, 8, 19, 27

    Estimate the standard deviation of the distances travelled by all customers of this restaurant.
    A. 50.86 miles
    B. 7.13 miles
    C. 44.5 miles
    D. 6.67 miles
    E. None of the above.
    Mr F says: Use the sample standard deviation as your estimate. Now read my above comments.
    ..
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  3. #3
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    Hi, which formula would u use? thanks!
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    Quote Originally Posted by chungkayan View Post
    Hi, which formula would u use? thanks!

     <br />
s= \sqrt{\frac{\sum(x-\bar{x})^2}{n-1}}<br />
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  5. #5
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    Quote Originally Posted by chungkayan View Post
    Hi, which formula would u use? thanks!
    The formula that is in your classnotes!
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  6. #6
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    Basically, to work out the first one, i found out the mean, and it was 71.75. After, i subtract the different numbers of 75,66,83,54,72,86,60,78 from the mean. (3.25,-5.75,11.25,-17.75,0.25,14.25,-11.75,6.25)

    After, i squared them, so its:
    10.5625, 33.0625, 126.5625,203.0625,0.0625,203.0625,138.0625.

    Adding up those numbers, it gives: 714.4375/7=102.0625

    square root 102.0625 to give 10.10259868

    but the answer isn't right. what did i do wrong?
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  7. #7
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    Your working seems fine, if this is not the answer then another derivation of standard deviation must be required. I am at a loss to explain this without further information.
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  8. #8
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    but its meant 2 be 10.40? so 0.30 away.
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  9. #9
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    Quote Originally Posted by chungkayan View Post
    but its meant 2 be 10.40? so 0.30 away.
    This could be due to some rounding error.
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    The manager of a restaurant has carried out a small-scale survey to find out how far customers travel to the restaurant. The results for a randomly selected sample of 8 customers were as follows (distances in miles):

    12, 23, 14, 27, 14, 8, 19, 27

    Estimate the standard deviation of the distances travelled by all customers of this restaurant.
    A. 50.86 miles
    B. 7.13 miles
    C. 44.5 miles
    D. 6.67 miles
    E. None of the above.
    is it possible to work this out for me? as i tried doing this, and i got 7.32900305. i know its not a massive difference, but if i didn't look at answer, i could of chose none of the above, please help. thanks!
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  11. #11
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    Quote Originally Posted by chungkayan View Post
    The manager of a restaurant has carried out a small-scale survey to find out how far customers travel to the restaurant. The results for a randomly selected sample of 8 customers were as follows (distances in miles):

    12, 23, 14, 27, 14, 8, 19, 27

    Estimate the standard deviation of the distances travelled by all customers of this restaurant.
    A. 50.86 miles
    B. 7.13 miles
    C. 44.5 miles
    D. 6.67 miles
    E. None of the above.
    is it possible to work this out for me? as i tried doing this, and i got 7.32900305. i know its not a massive difference, but if i didn't look at answer, i could of chose none of the above, please help. thanks!
    If you look at the spread of the data it cannot be options A or C. The question says 'estimate', with the answer you found option B could be an estimate.
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  12. #12
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    Oh, i get why i cant get it now. but how do u estimate? how do u know its not 6.67 or none of the above but 7.13? is there a way to estimate s.d.? please help. thanks
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