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.
What is the median of the ratings given by R3 to the five workers?[This question was asked as TITA]

• A. 4
• B. 3
• C. 2
• D. 1

Answer 1

The Correct Option is A

The task is to determine the median of the ratings given by R3 to the five workers—Ullas, Vasu, Waman, Xavier, and Yusuf.

1. The mean rating of R3 is 3.8. So, the total sum of the ratings is:
   $3.8 \times 5 = 19$ 
2. From the given information:
   
   • R3 gave a rating of 5 to Waman and Xavier
   • R3 gave a rating of 1 to Yusuf
3. Let the ratings given to Ullas and Vasu be $x$ and $y$ respectively.
4. Total of all ratings:
   $5 + 5 + 1 + x + y = 19$
   So, $x + y = 8$
5. We are told that Vasu has:
   • Mean rating = 3.8
   • Median = 4
   • Mode = 4
   • Range = 3
6. Then $x = 8 - 4 = 4$ (Ullas gets a rating of 4)
7. Now, R3’s ratings are: 4, 4, 5, 5, 1
8. Sorted ratings: 1, 4, 4, 5, 5
9. Median is the middle value = 4

Final Answer: 4