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 rating did R1 give to Xavier? [This question was asked as TITA]

• A. 2
• B. 3
• C. 1
• D. 0

Answer 1

The Correct Option is B

To determine R1's rating for Xavier, the following data is analyzed:

• R1's average rating is 3.4.
• R1's ratings are integers between 1 and 5, inclusive.
• R1 rated Waman 5 and Ullas 1.
• For an average rating of 3.4 across 5 individuals, the total sum of ratings from R1 is calculated as: \(3.4 \times 5 = 17\).
• Let R1's ratings for Ullas, Vasu, Waman, Xavier, and Yusuf be represented by \(R1_U, R1_V, R1_W, R1_X, R1_Y\) respectively.

Given the following:

• \(R1_U = 1\)
• \(R1_W = 5\)

Substituting the known values into the total sum equation:

• \(1 + R1_V + 5 + R1_X + R1_Y = 17\)
• This simplifies to: \(R1_V + R1_X + R1_Y = 11\)

The objective is to find \(R1_X\) (Xavier's rating). Considering the mean ratings for workers:

• Ullas: Mean rating = 2.2, Total ratings = \(2.2 \times 5 = 11\) (consistent with R1's rating of 1).
• Xavier: Mean rating = 3.6, Total ratings = \(3.6 \times 5 = 18\).

A combination for \(R1_V + R1_X + R1_Y = 11\) must be found where each rating is an integer between 1 and 5.

• An example of a valid combination is: \(R1_V = 4, R1_X = 3, R1_Y = 4\).
• This combination satisfies the condition: \(4 + 3 + 4 = 11\) and all ratings are within the [1, 5] range.

Based on this analysis, R1 assigned Xavier a rating of 3.