CAT 2023 Slot 1 — DILR Question 20
Answer the following questions based on the information given below:
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.
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* 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.
Which among the following restaurants gave its median rating to exactly one of the workers?
Answer & solution
- A
R5
R4
- C
R2
- D
R3
Easy
For each restaurant, find its median rating (the middle of its sorted row), then count how many workers actually received that exact value. We want the restaurant where that count is exactly .
Each restaurant's five ratings, sorted, with median highlighted:
| Restaurant | Sorted ratings | Median | How many got it |
|---|---|---|---|
| R1 | 1, 3, 4, 4, 5 | 4 | 2 |
| R2 | 1, 1, 2, 2, 5 | 2 | 2 |
| R3 | 1, 4, 4, 5, 5 | 4 | 2 |
| R4 | 1, 2, 3, 4, 4 | 3 | 1 |
| R5 | 2, 2, 4, 4, 5 | 4 | 2 |
R1, R2, R3 and R5 each have their median value appearing twice in the row. Only R4, with median , gave a to exactly one worker (Yusuf).
Option (b): .