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Math Help - Frequency problem

  1. #1
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    Frequency problem

    1. An ice-cream manufacturing company has developed a new flavour of ice-cream. In order to gather feedback on the new flavour, they conducted a taste test. Each person was asked to rate the taste of this new flavour on a scale of 1 to 7, with 7 being excellent taste and 1 being bad taste as follows:


    (bad taste) 1 2 3 4 5 6 7 (excellent taste)



    On the first day, a group comprising of 3 persons were asked to take the taste test. After gathering their feedback, the estimated mean and standard deviation of the ratings were computed. A mean of 4 and a standard deviation of 0 were obtained.
    • What is the rating given by each of these 3 persons?

    • On the second day, another 15 persons were given the taste test. The feedback gathered from the total random sample of 18 persons is shown in the frequency table below:
    Rating
    1
    2
    3
    4
    5
    6
    7
    Frequency
    3
    7
    3
    3
    1
    1
    0

    • What is the estimated mean of the ratings?

    • What is the estimated standard deviation of the ratings?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by dorwei92 View Post
    1. An ice-cream manufacturing company has developed a new flavour of ice-cream. In order to gather feedback on the new flavour, they conducted a taste test. Each person was asked to rate the taste of this new flavour on a scale of 1 to 7, with 7 being excellent taste and 1 being bad taste as follows:


    (bad taste) 1 2 3 4 5 6 7 (excellent taste)






    On the first day, a group comprising of 3 persons were asked to take the taste test. After gathering their feedback, the estimated mean and standard deviation of the ratings were computed. A mean of 4 and a standard deviation of 0 were obtained.
    • What is the rating given by each of these 3 persons?
    SD of zero means all the ratings were the same, so what do think those rating were if their mean was 4?




    • On the second day, another 15 persons were given the taste test. The feedback gathered from the total random sample of 18 persons is shown in the frequency table below:
    Rating








    1




    2




    3




    4




    5




    6




    7




    Frequency




    3




    7




    3




    3




    1




    1




    0







    • What is the estimated mean of the ratings?

    • What is the estimated standard deviation of the ratings?

    m=\sum_{r=1}^n r \rho(r)

    where \rho(r)=f(r)/\left[\sum_{r=1}^n f(r)\right]

    and:

     <br />
s^2=\sum_{r=1}^n (r-m)^2 \rho (r)<br />

    CB
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