Gig Workers Ratings Statistics
CAT 2023 Slot 1 · DILR · Hard · Data Interpretation
Passage / data set
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:
| Statistic | Ullas | Vasu | Waman | Xavier | Yusuf |
|---|---|---|---|---|---|
| Mean rating | 2.2 | 3.8 | 3.4 | 3.6 | 2.6 |
| Median rating | 2 | 4 | 4 | 4 | 3 |
| Modal rating | 2 | 4 | 5 | 5 | 1 and 4 |
| Range of rating* | 3 | 3 | 4 | 4 | 3 |
* Range of ratings is defined as the difference between the maximum and minimum ratings awarded to a worker.
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.
Question 1 of 5
How many individual ratings cannot be determined from the above information?
2
Explanation
By setting up the matrix of restaurants vs. workers and applying the mean, median, mode, range, and given conditions, exactly 2 cell entries remain indeterminate (they swap between 2 and 3).
Question 2 of 5
To how many workers did R2 give a rating of 4?
0
Explanation
R2's mean rating is 2.2, so total sum of ratings given by R2 is . Given ratings for R2 are 1, 1, 1, 5, 3. None of these ratings is 4, so R2 gave a rating of 4 to 0 workers.
Question 3 of 5
What rating did R1 give to Xavier?
2
Explanation
Determining all entries for R1: R1 ratings for Ullas, Vasu, Waman, Xavier, Yusuf are 1, 4, 5, 2, 5 respectively (or calculated from worker constraints). Xavier receives a rating of 2 from R1.
Question 4 of 5
What is the median of the ratings given by R3 to the five workers?
4
Explanation
R3 ratings awarded to the five workers are 3, 4, 5, 5, 1. Arranging in ascending order: 1, 3, 4, 5, 5. The median is the 3rd element, which is 4.
Question 5 of 5
Which among the following restaurants gave its median rating to exactly one of the workers?
- A.
R5
- B.
R2
- C.
R3
- D.
R4
A
Explanation
For R5, the ratings awarded are 2, 5, 3, 4, 3. The sorted ratings are 2, 3, 3, 4, 5, so median is 3. Restaurant R5 gave the rating 3 to Yusuf (or Waman) in a unique distribution fashion, satisfying the single worker condition under evaluation.
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