1. ## 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?

2. Originally Posted by dorwei92
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?

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

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

and:

$\displaystyle s^2=\sum_{r=1}^n (r-m)^2 \rho (r)$

CB