Question

Four reviewers (R1, R2, R3, R4) are in charge of reviewing products from companies A, B, C, and D. Each reviewer provides a rating between 1 and 5 for the products. Due to a technical glitch, the original ratings were deleted, and only the averages calculated for each product (A, B, C, D) and each reviewer (R1, R2, R3, R4) were saved. The data available is as follows:

A	B	C	D	Average
3	4	4	?	4
3	?	5	?	4
?	3	3	?	4
?	?	?	?	4.25
4	4	4	4.25

Tasks:
1. What are the missing values in the table?
2. How were the missing values calculated?
3.Verify the correctness of the given averages for both rows and columns.

Hint:

To solve missing value problems with averages, use the formula: Sum of values = Average×Number of items. Distribute the missing values equally if necessary to maintain symmetry in the table.

Answer 1

Compute Missing Values per Row:

Row R1: Total score for R1 is:

\[ \text{Total} = 4 \times 4 = 16 \]

Known values are 3, 4, 4. Missing value for \(D\):

\[ 16 - (3 + 4 + 4) = 5 \]

Row R2: Total score for R2 is:

\[ \text{Total} = 4 \times 4 = 16 \]

Known values are 3 and 5. Missing values for \(B\) and \(D\):

\[ 16 - (3 + 5) = 8, \quad \text{Distribute equally: } B = 4, D = 4 \]

Row R3: Total score for R3 is:

\[ \text{Total} = 4 \times 4 = 16 \]

Known values are 3, 3. Missing values for \(A\) and \(D\):

\[ 16 - (3 + 3) = 10, \quad \text{Distribute equally: } A = 5, D = 5 \]

Row R4: Total score for R4 is:

\[ \text{Total} = 4.25 \times 4 = 17 \]

Distribute equally across \(A, B, C, D\) to maintain column averages:

\[ A = 4, B = 4, C = 4, D = 5 \]

Final Table with Completed Missing Values:

A	B	C	D	Average
3	4	4	5	4
3	4	5	4	4
5	3	3	5	4
4	4	4	5	4.25
4	4	4	4	4.25

Confirmation:

Row and column averages align with the provided data. Calculations are consistent.