I don't need you to solve the below problem. Rather, I need help understanding how the solution for the below question was calculated. To begin, the below question is the complete original question (and below that is the solution, and you'll see my actual problem at the very bottom of this post):

a. Columns A & B - In a taste test of a new beer 100 people rated the new beer and the leading brand on the market. The possible ratings were Poor, Fair, Good, Very good, and Excellent. The responses for the new beer and the leading beer were recorded using a 1-2-3-4-5 coding system. Can we infer that the new beer is more highly rated than the leading brand?

b. Columns C & D - The responses were recoded so that 3 = Poor, 8 = Fair, 22 = Good, 37 = Very good, and 55 = Excellent. Can we infer that the new beer is more highly rated than the leading brand?

c. Why are the answers to Parts (a) and (b) identical?

Column A	Column B	Column C	Column D
New	Leading	New	Leading
5	4	55	37
4	3	37	22
4	4	37	37
4	5	37	55
4	4	37	37
4	3	37	22
4	4	37	37
3	2	22	8
4	5	37	55
3	2	22	8
2	2	8	8
3	2	22	8
1	1	3	3
3	4	22	37
4	3	37	22
5	5	55	55
5	4	55	37
4	2	37	8
4	4	37	37
4	3	37	22
5	3	55	22
2	4	8	37
4	3	37	22
5	4	55	37
2	2	8	8
4	3	37	22
3	4	22	37
4	5	37	55
4	3	37	22
3	3	22	22
3	3	22	22
2	1	8	3
3	2	22	8
2	3	8	22
5	4	55	37
4	3	37	22
3	4	22	37
4	2	37	8
5	4	55	37
5	5	55	55
3	2	22	8
5	3	55	22
4	3	37	22
1	1	3	3
3	1	22	3
5	4	55	37
4	3	37	22
3	2	22	8
4	4	37	37
4	5	37	55
5	5	55	55
4	4	37	37
5	3	55	22
3	4	22	37
3	3	22	22
3	3	22	22
4	5	37	55
3	4	22	37
5	4	55	37
3	3	22	22
4	4	37	37
4	5	37	55
3	4	22	37
3	4	22	37
4	5	37	55
3	4	22	37
5	3	55	22
4	3	37	22
3	2	22	8
4	5	37	55
4	4	37	37
3	2	22	8
5	4	55	37
4	3	37	22
4	5	37	55
4	5	37	55
4	2	37	8
4	5	37	55
4	5	37	55
3	4	22	37
4	3	37	22
5	3	55	22
3	4	22	37
4	5	37	55
5	5	55	55
3	4	22	37
4	3	37	22
4	3	37	22
3	4	22	37
3	1	22	3
5	4	55	37
3	4	22	37
4	3	37	22
3	3	22	22
4	3	37	22
4	4	37	37
4	3	37	22
4	4	37	37
1	2	3	8
4	5	37	55

SOLUTION:

The use of Spearman's rho as non parametric test to this table is the most appropriate. Since the gathered data are based on a Likert scale (1,2,345) ordered and ranked based on a given interval and characteristics, Spearman's rho should be used to interpret the data.

1. Yes, it can easily be inferred that new beer is more highly rated than the leading brand. As 5 as the highest and most favorable choice, getting the average of Column A will fall into the interval of 4.20-5.00

2. Yes, same with the first item. Based on the gathered data, most of the responses are 55 and it is the highest and most favorable choice. Getting the average for column C, it will also fall in the interval 4.20-5.00

3. They have the same answer because they use the same values for their Likert scale.

1-Poor

2-Fair

3-Good

4-Very Good

5-Excellent

Even if A and C used other values (3,8,22,37,55) it doesn't change the categorical response meaning of Poor, Fair, Good, Very Good and Excellent respectively.

Explanation:

Step 1: Identify what is the best non parametric test to be used

Step 2: Simply calculate the mean, by adding up the numbers divided by the number of scores added

Step 3: compare their averages

Step 4: interpret using an interval

1 = 1.00-1.80

2 = 1.81-2.60

3 = 2.61-3.40

4 = 3.41-4.20

5 = 4.21-5.00

If the average is 4.34 it falls within 4.21-5.00 so it is interpreted as 5.

ACTUAL PROBLEM (WHAT I NEED HELP WITH): How do you calculate Step 4 above? When I calculated the mean and divided it by the number of score for all of the 1's in column A, it equaled 1. The same thing happened with the 2's in column A, the 3's all the way up to the 5's in column A. Would you please show me how it's properly calculated? And, how was the 4.34 average calculated?