Question

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.

	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

* 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.
To how many workers did R2 give a rating of 4?[This question was asked as TITA]

• A. 3
• B. 1
• C. 0
• D. 2

Answer 1

The Correct Option is C

The problem involves analyzing ratings given by five restaurants to five workers under various constraints. We need to determine how many workers received a rating of 4 from Restaurant R2.

1. Understand the Given Data:

   	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

   • R1 Mean = 3.4, R2 Mean = 2.2, R3 Mean = 3.8, R4 Mean = 2.8, R5 Mean = 3.4.
2. Analyze Given Conditions:
   • R2 rated Xavier and Waman 5 (Waman's ratings by R1 and Xavier's by R2 and R3).
   • R2 rated Waman and Yusuf 1.
   • Known R2 Ratings: 5 for Xavier, 1 for Waman and Yusuf.
3. Calculate Missing Values:
   • R2 Mean is 2.2. Assume five ratings R2 gives are a, 1, 5, 1, 1.
   • (a + 1 + 5 + 1 + 1)/5 = 2.2; 7 + a = 11 ➜ a = 4, no 4 required as a rating by R2, considering available information.
4. Conclusion: There are no workers to whom R2 gave a rating of 4. Answer: 0