The summary statistics of these ratings for the five workers is given below.
| Ullas | Vasu | Waman | Xavier | Yusuf | |
|---|---|---|---|---|---|
| Mean rating | 2.2 | 3.8 | 3.4 | 3.6 | 2.6 |
| Median rating | 2 | 4 | 4 | 4 | 3 |
| Model rating | 2 | 4 | 5 | 5 | 1 and 4 |
| Range of rating | 3 | 3 | 4 | 4 | 3 |
The following is partial information about ratings of 1 and 5 awarded by the restaurants to the workers.
(a) R1 awarded a rating of 5 to Waman, as did R2 to Xavier, R3 to Waman and Xavier, and R5 to Vasu.
(b) R1 awarded a rating of 1 to Ullas, as did R2 to Waman and Yusuf, and R3 to Yusuf.
How many individual ratings cannot be determined from the above information?
Solution and Explanation
The average ratings provided by R1, R2, R3, R4, and R5 are as follows:
- R1: \( 5 \times 3.4 = 17 \)
- R2: \( 5 \times 2.2 = 11 \)
- R3: \( 5 \times 3.8 = 19 \)
- R4: \( 5 \times 2.8 = 14 \)
- R5: \( 5 \times 3.4 = 17 \)
The total ratings for each movie are:
- U: \( 5 \times 2.2 = 11 \)
- V: \( 5 \times 3.8 = 19 \)
- W: \( 5 \times 3.4 = 17 \)
- X: \( 5 \times 3.6 = 18 \)
- Y: \( 5 \times 2.6 = 13 \)
The matrix below shows the known rating values:
| R1 | R2 | R3 | R4 | R5 | Total | |
|---|---|---|---|---|---|---|
| U | 1 | 2 | 4 | 2 | 2 | 11 |
| V | 4 | 2 | 4 | 4 | 5 | 19 |
| W | 5 | 1 | 5 | 4 | 2 | 17 |
| X | 3 | 5 | 5 | 1 | 4 | 18 |
| Y | 4 | 1 | 1 | 3 | 4 | 13 |
| Total | 17 | 11 | 19 | 14 | 17 |
Conclusion: Since all ratings are uniquely determined, the count of entries that can still be uniquely determined is 0.
Answer: \( \boxed{0} \)
To how many workers did R2 give a rating of 4?
Solution and Explanation
Based on the average ratings provided by R1, R2, R3, R4, and R5 as 3.4, 2.2, 3.8, 2.8, and 3.4 respectively, the total sum of ratings for each rater can be computed as follows:
- R1: 5 ratings × 3.4 average = 17
- R2: 5 ratings × 2.2 average = 11
- R3: 5 ratings × 3.8 average = 19
- R4: 5 ratings × 2.8 average = 14
- R5: 5 ratings × 3.4 average = 17
Similarly, the sum of ratings received by items U, V, W, X, and Y are:
- U: 5 ratings × 2.2 average = 11
- V: 5 ratings × 3.8 average = 19
- W: 5 ratings × 3.4 average = 17
- X: 5 ratings × 3.6 average = 18
- Y: 5 ratings × 2.6 average = 13
This information can be organized into a table. The following table represents this partial data:
| U | V | W | X | Y | Sum | |
|---|---|---|---|---|---|---|
| R1 | a | b | c | d | e | 17 |
| Sum | 11 | 19 | 17 | 18 | 13 |
Rater R2 provided the ratings 1, 1, 2, 2, 5.
He rated 0 workers.
What rating did R1 give to Xavier?
Solution and Explanation
Given the average ratings provided by raters R1, R2, R3, R4, and R5 as 3.4, 2.2, 3.8, 2.8, and 3.4 respectively, the total sum of ratings from each rater can be computed as follows:
- R1: 5 × 3.4 = 17
- R2: 5 × 2.2 = 11
- R3: 5 × 3.8 = 19
- R4: 5 × 2.8 = 14
- R5: 5 × 3.4 = 17
Similarly, the total ratings received by items U, V, W, X, and Y are:
- U: 5 × 2.2 = 11
- V: 5 × 3.8 = 19
- W: 5 × 3.4 = 17
- X: 5 × 3.6 = 18
- Y: 5 × 2.6 = 13
This information can be presented in a table. The following table shows this partial data:
| U | V | W | X | Y | Sum | |
|---|---|---|---|---|---|---|
| R1 | a | b | c | d | e | 17 |
| Sum | 11 | 19 | 17 | 18 | 13 |
The variables 𝑎,𝑏,𝑐,…,𝑦a,b,c,…,y denote the individual ratings given by each rater for each item. The sums at the end of each row indicate the total ratings provided by each rater, while the sums at the bottom of each column indicate the total ratings received by each item.
Regarding item U: Given a median of 2, a mode of 2, and a range of 3:
- The ratings should be structured as 1, a, 2, b, 4, with 'a' and 'b' being unknown values.
- The total sum of U's ratings is 11, as previously calculated.
- To satisfy the mode of 2, both 'a' and 'b' must be 2.
- Consequently, U's ratings are determined to be 1, 2, 2, 2, 4.
Regarding item V: Given a median of 4, a mode of 4, and a range of 3:
- The ratings should be structured as 2, a, 4, b, 5, with 'a' and 'b' being unknown values.
- The total sum of V's ratings is 19, as previously calculated.
- To satisfy the mode of 4, both 'a' and 'b' must be 4.
- Therefore, V's ratings are determined to be 2, 4, 4, 4, 5.
Regarding item W: Given a median of 4, a mode of 5, and a range of 4:
- The ratings should be structured as 1, a, 4, 5, 5, with 'a' being an unknown value.
- The total sum of W's ratings is 17, as previously calculated.
- Solving for 'a', we find it to be 2.
- Thus, W's ratings are determined to be 1, 2, 4, 5, 5.
Regarding item X: Given a median of 4, a mode of 5, and a range of 4:
- The ratings should be structured as 1, a, 4, 5, 5, with 'a' being an unknown value.
- The total sum of X's ratings is 18, as previously calculated.
- Solving for 'a', we find it to be 3.
- Therefore, X's ratings are determined to be 1, 3, 4, 5, 5.
Regarding item Y: Given a median of 3, modes of 1 and 4, and a range of 3:
- The ratings should be structured as 1, a, 3, b, 4, with 'a' and 'b' being unknown values.
- The total sum of Y's ratings is 13, as previously calculated.
- We need to determine the values of 'a' and 'b'.
- Considering the modes, both 'a' and 'b' must be either 1 or 4.
- However, the range requires the difference between the highest and lowest ratings to be 3.
- Thus, Y's ratings are determined to be 1, 1, 3, 4, 4.
Observing column R3, the two missing entries must sum to 8. The only possible combination is 4 + 4. Therefore, we can assign 4 to row U and 4 to row V.
Examining column R1, the missing elements must sum to 17−5−4−1=7. The possible pairs are 3 + 4 or 4 + 3.
Now, considering column R5, the missing elements must sum to 10. The combination 4 + 3 + 3 is not viable as it conflicts with the possible combinations for column R1. Thus, the combination must be 2 + 4 + 4.
We can assign the values 3 + 4 to column R1, and the remaining values will fill column R4. This allows for the completion of the table:
| R1 | R2 | R3 | R4 | R5 | Total | |
| U | 1 | 2 | 4 | 2 | 2 | 11 |
| V | 4 | 2 | 4 | 4 | 5 | 19 |
| W | 5 | 1 | 5 | 4 | 2 | 17 |
| X | 3 | 5 | 5 | 1 | 4 | 18 |
| Y | 4 | 1 | 1 | 3 | 4 | 13 |
| Total | 17 | 11 | 19 | 14 | 17 |
From the completed table, it is evident that R1 assigned a rating of 3 to item X.
Therefore, the correct answer is 3.
What is the median of the ratings given by R3 to the five workers?
Solution and Explanation
The sum of ratings for reviewers R1, R2, R3, R4, and R5, based on their average ratings of 3.4, 2.2, 3.8, 2.8, and 3.4 respectively, is calculated as 5 times their respective means:
- R1: 5 × 3.4 = 17
- R2: 5 × 2.2 = 11
- R3: 5 × 3.8 = 19
- R4: 5 × 2.8 = 14
- R5: 5 × 3.4 = 17
Similarly, the sum of ratings received by users U, V, W, X, and Y, based on their average ratings of 2.2, 3.8, 3.4, 3.6, and 2.6 respectively, is calculated as 5 times their respective means:
- U: 5 × 2.2 = 11
- V: 5 × 3.8 = 19
- W: 5 × 3.4 = 17
- X: 5 × 3.6 = 18
- Y: 5 × 2.6 = 13
Consolidating the data from partial information (a) and (b) into a table yields:
| R1 | R2 | R3 | R4 | R5 | Total | Missing Entries | |
|---|---|---|---|---|---|---|---|
| U | 1 | 2 | 4 | 2 | 2 | 11 | |
| V | 4 | 2 | 4 | 4 | 5 | 19 | |
| W | 5 | 1 | 5 | 4 | 2 | 17 | |
| X | 3 | 5 | 5 | 1 | 4 | 18 | |
| Y | 4 | 1 | 1 | 3 | 4 | 13 | |
| Total | 17 | 11 | 19 | 14 | 17 | - |
Median analysis:
- R2's median rating is 2, assigned to 2 workers.
- R5's median rating is 4, assigned to 2 workers.
- R4's median rating is 3, assigned to 1 worker.
- R3's median rating is 4, assigned to 2 workers.
Correct option: (C) R4
Which among the following restaurants gave its median rating to exactly one of the workers?
Show Hint
R2 median rating is 2 = given to 2 workers
R5 median rating is 4 = given to 2 workers
R4 median rating is 3 = given to only 1 worker.
R3 median rating is 4 = given to 2 workers
- R3
- R5
- R4
- R2
The Correct Option is C
Solution and Explanation
The sum of ratings for reviewers R1, R2, R3, R4, and R5, based on an average of 5 ratings each, are: R1: 17 (5 × 3.4), R2: 11 (5 × 2.2), R3: 19 (5 × 3.8), R4: 14 (5 × 2.8), and R5: 17 (5 × 3.4).
- R1: 5 × 3.4 = 17
- R2: 5 × 2.2 = 11
- R3: 5 × 3.8 = 19
- R4: 5 × 2.8 = 14
- R5: 5 × 3.4 = 17
Similarly, the sum of ratings received by recipients U, V, W, X, and Y, based on an average of 5 ratings each, are: U: 11 (5 × 2.2), V: 19 (5 × 3.8), W: 17 (5 × 3.4), X: 18 (5 × 3.6), and Y: 13 (5 × 2.6).
- U: 5 × 2.2 = 11
- V: 5 × 3.8 = 19
- W: 5 × 3.4 = 17
- X: 5 × 3.6 = 18
- Y: 5 × 2.6 = 13
The provided partial data is presented in the following table:
| R1 | R2 | R3 | R4 | R5 | Total | Missing Entries | |
|---|---|---|---|---|---|---|---|
| U | 1 | 2 | 4 | 2 | 2 | 11 | |
| V | 4 | 2 | 4 | 4 | 5 | 19 | |
| W | 5 | 1 | 5 | 4 | 2 | 17 | |
| X | 3 | 5 | 5 | 1 | 4 | 18 | |
| Y | 4 | 1 | 1 | 3 | 4 | 13 | |
| Total | 17 | 11 | 19 | 14 | 17 | - |
The median rating given by R2 is 2, assigned to 2 workers. R5's median rating is 4, given to 2 workers. R4's median rating is 3, given to only 1 worker. R3's median rating is 4, given to 2 workers.
- R2's median rating is 2, given to 2 workers.
- R5's median rating is 4, given to 2 workers.
- R4's median rating is 3, given to only 1 worker.
- R3's median rating is 4, given to 2 workers.
Therefore, the correct option is (C): R4.
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5. P1 contained double the amount of protein that M3 contains. - Five restaurants, coded R1, R2, R3, R4 and R5 gave integer ratings to five gig workers – Ullas, Vasu, Waman, Xavier and Yusuf, on a scale of 1 to 5. The means of the ratings given by R1, R2, R3, R4 and R5 were 3.4, 2.2, 3.8, 2.8 and 3.4 respectively.
The summary statistics of these ratings for the five workers is given below.* Range of ratings is defined as the difference between the maximum and minimum ratings awarded to a worker.Ullas Vasu Waman Xavier Yusuf Mean rating 2.2 3.8 3.4 3.6 2.6 Median rating 2 4 4 4 3 Model rating 2 4 5 5 1 and 4 Range of rating 3 3 4 4 3
The following is partial information about ratings of 1 and 5 awarded by the restaurants to the workers.
(a) R1 awarded a rating of 5 to Waman, as did R2 to Xavier, R3 to Waman and Xavier, and R5 to Vasu.
(b) R1 awarded a rating of 1 to Ullas, as did R2 to Waman and Yusuf, and R3 to Yusuf.
What is the median of the ratings given by R3 to the five workers?[This question was asked as TITA] - Want to practice more? Try solving extra ecology questions todayView All Questions