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

Calculate Missing Values for Each Row:

For R1: The total score for R1 is:

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

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

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

For R2: The total score for R2 is:

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

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

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

For R3: The total score for R3 is:

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

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

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

For R4: The total score for R4 is:

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

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

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

Final Table with Missing Values Filled:

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	4.25

Verification:

Row and column averages match the given data. The calculations are consistent.