Question:medium
Four reviewers (R1, R2, R3, R4) are in charge of reviewing products from companies A, B, C, and D. Each reviewer provides a rating between 1 and 5 for the products. Due to a technical glitch, the original ratings were deleted, and only the averages calculated for each product (A, B, C, D) and each reviewer (R1, R2, R3, R4) were saved. The data available is as follows:A B C D Average 3 4 4 ? 4 3 ? 5 ? 4 ? 3 3 ? 4 ? ? ? ? 4.25 4 4 4 4.25
Tasks:
1. What are the missing values in the table?
2. How were the missing values calculated?
3.Verify the correctness of the given averages for both rows and columns.
Four reviewers (R1, R2, R3, R4) are in charge of reviewing products from companies A, B, C, and D. Each reviewer provides a rating between 1 and 5 for the products. Due to a technical glitch, the original ratings were deleted, and only the averages calculated for each product (A, B, C, D) and each reviewer (R1, R2, R3, R4) were saved. The data available is as follows:
Tasks:
1. What are the missing values in the table?
2. How were the missing values calculated?
3.Verify the correctness of the given averages for both rows and columns.
| A | B | C | D | Average |
|---|---|---|---|---|
| 3 | 4 | 4 | ? | 4 |
| 3 | ? | 5 | ? | 4 |
| ? | 3 | 3 | ? | 4 |
| ? | ? | ? | ? | 4.25 |
| 4 | 4 | 4 | 4.25 |
1. What are the missing values in the table?
2. How were the missing values calculated?
3.Verify the correctness of the given averages for both rows and columns.
Show Hint
To solve missing value problems with averages, use the formula: Sum of values = Average×Number of items. Distribute the missing values equally if necessary to maintain symmetry in the table.
Updated On: Jan 13, 2026
Show Solution
Solution and Explanation
Compute Missing Values per Row:
Row R1: Total score for R1 is:
\[ \text{Total} = 4 \times 4 = 16 \]
Known values are 3, 4, 4. Missing value for \(D\):
\[ 16 - (3 + 4 + 4) = 5 \]
Row R2: Total score for R2 is:
\[ \text{Total} = 4 \times 4 = 16 \]
Known values are 3 and 5. Missing values for \(B\) and \(D\):
\[ 16 - (3 + 5) = 8, \quad \text{Distribute equally: } B = 4, D = 4 \]
Row R3: Total score for R3 is:
\[ \text{Total} = 4 \times 4 = 16 \]
Known values are 3, 3. Missing values for \(A\) and \(D\):
\[ 16 - (3 + 3) = 10, \quad \text{Distribute equally: } A = 5, D = 5 \]
Row R4: Total score for R4 is:
\[ \text{Total} = 4.25 \times 4 = 17 \]
Distribute equally across \(A, B, C, D\) to maintain column averages:
\[ A = 4, B = 4, C = 4, D = 5 \]
Final Table with Completed Missing Values:
| A | B | C | D | Average |
|---|---|---|---|---|
| 3 | 4 | 4 | 5 | 4 |
| 3 | 4 | 5 | 4 | 4 |
| 5 | 3 | 3 | 5 | 4 |
| 4 | 4 | 4 | 5 | 4.25 |
| 4 | 4 | 4 | 4 | 4.25 |
Confirmation:
Row and column averages align with the provided data. Calculations are consistent.
Was this answer helpful?
0
Top Questions on Table
- 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.* Range of ratings is defined as the difference between the maximum and minimum ratings awarded to a worker.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
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. - Odsville has five firms – Alfloo, Bzygoo, Czechy, Drjbna and Elavalaki. Each of these firms was founded in some year and also closed down a few years later.
Each firm raised Rs. 1 crore in its first and last year of existence. The amount each firm raised every year increased until it reached a maximum, and then decreased until the firm closed down. No firm raised the same amount of money in two consecutive years. Each annual increase and decrease was either by Rs. 1 crore or by Rs. 2 crores.
The table below provides partial information about the five firms.Firm First year of existence Last year of existence Total amount raised (Rs. crores) Alfloo 2009 2016 21 Bzygoo 2012 2015 Czechy 2013 9 Drjbna 2011 2015 10 Elavalaki 2010 13 - Three participants – Akhil, Bimal and Chatur participate in a random draw competition for five days. Every day, each participant randomly picks up a ball numbered between 1 and 9. The number on the ball determines his score on that day. The total score of a participant is the sum of his scores attained in the five days. The total score of a day is the sum of participants’ scores on that day. The 2-day average on a day, except on Day 1, is the average of the total scores of that day and of the previous day. For example, if the total scores of Day 1 and Day 2 are 25 and 20, then the 2-day average on Day 2 is calculated as 22.5. Table 1 gives the 2-day averages for Days 2 through 5.Participants are ranked each day, with the person having the maximum score being awarded the minimum rank (1) on that day. If there is a tie, all participants with the tied score are awarded the best available rank. For example, if on a day Akhil, Bimal, and Chatur score 8, 7 and 7 respectively, then their ranks will be 1, 2 and 2 respectively on that day. These ranks are given in Table 2.
Table 1: 2-day averages for Days through 5 Day 2 Day 3 Day 4 Day 5 15 15.5 16 17 The following information is also known.Table 2 : Ranks of participants on each day Day 1 Day 2 Day 3 Day 4 Day 5 Akhil 1 2 2 3 3 Bimal 2 3 2 1 1 Chatur 3 1 1 2 2
1. Chatur always scores in multiples of 3. His score on Day 2 is the unique highest score in the competition. His minimum score is observed only on Day 1, and it matches Akhil’s score on Day 4.
2. The total score on Day 3 is the same as the total score on Day 4.
3. Bimal’s scores are the same on Day 1 and Day 3. - Odsville has five firms – Alfloo, Bzygoo, Czechy, Drjbna and Elavalaki. Each of these firms was founded in some year and also closed down a few years later.
Each firm raised Rs. 1 crore in its first and last year of existence. The amount each firm raised every year increased until it reached a maximum, and then decreased until the firm closed down. No firm raised the same amount of money in two consecutive years. Each annual increase and decrease was either by Rs. 1 crore or by Rs. 2 crores.
The table below provides partial information about the five firms.What is the largest possible total amount of money (in Rs. crores) that could have been raised in 2013? (This Question was asked as TITA)Firm First year of existence Last year of existence Total amount raised (Rs. crores) Alfloo 2009 2016 21 Bzygoo 2012 2015 Czechy 2013 9 Drjbna 2011 2015 10 Elavalaki 2010 13 - Want to practice more? Try solving extra ecology questions todayView All Questions
Questions Asked in XAT exam
Applicants have been shortlisted for interviews for some data analyst positions. Some of the applicants have advanced expertise in one or more fields among the following: data analysis, database handling and coding. The numbers of applicants with different advanced expertise are given in the 2 × 8 table below.
The number of applicants with advanced expertise in all three fields is given as x in the table, where x is a non-negative integer.
The number of applicants with advanced expertise in all three fields is given as x in the table, where x is a non-negative integer.
- XAT - 2024
- Data Interpretation