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Table Analysis

What is a table?
A table is an array of data displayed in columns and rows.
 
Did you know: On the actual test, tables can be sorted by columns (in either ascending order or descending order), by characters, or by numerical values.
 
Ascending order in characters means A to Z, while descending means the opposite direction. So, AZ would appear first in ascending order before BA or ZA.
 
Ascending order in numerical value means 0 to 9. So, in ascending order, 18 would appear before than 81 or 21.
 
Even a table is a graphic. The protocol of the graphic called table states that you can relate data across the rows or you might as well use a table as a menu. Some common tasks with tables are
  • Determine statistics such as mean, median, mode, or range
  • Determine ratios, proportions, or probabilities
  • Identify correlations between two sets of data
  • Compare an entry’s rank in two or more of the table’s categories
Example

The tables below provide the complete semantics of a Common Entrance Test (CET) conducted in different years.

Table showing the Number of Questions

 
Exam Quantitative Verbal Analytical
CET 1990 55 55 55
CET 1991 50 50 50
CET 1992 50 50 50
CET 1993 50 50 50
CET 1994 37 50 39


* Each question carries 1 mark.

General information on the Exams

 
Exam Total Duration
(in minutes)
Number of Questions Overall cutoff mark as a
percentage of maximum mark for the top five institutes
CET 1990 120 44 55
CET 1991 120 48 68
CET 1992 120 48 65
CET 1993 120 48 60
CET 1994 150 71 68


* The Difficulty Factor of the exam is the sum of the products of the number of questions of each type and the corresponding difficulty level. The Stress Factor is the Difficulty Factor divided by the Average Time Per Question.

Measure of Difficulty and Cut-offs

 

Exam

Quantitative

Verbal

Analytical

CET 1990

3, 9

3, 16

2, 12

CET 1991

2, 14

1, 19

1, 20

CET 1992

3, 11

1, 18

3, 14

CET 1993

3, 10

1, 18

2, 15

CET 1994

3, 8

1, 18

3, 9

 

* The Difficulty Factor of the exam is the sum of the products of the number of questions of each type and the corresponding difficulty level. The Stress Factor is the Difficulty Factor divided by the Average Time Per Question.

 

Solution Setup:

All the tables above and all the text available can be integrated into the following single structured table:
 

Exam

Area

Questions

Marks per question

Total Duration (in minute)

Average time per question (in seconds)

Difficulty level

1 = Easy

2 = Average

3 = Difficult

Area wise Cut-off Scores

Overall cutoff mark as a percentage of maximum mark for the top five Institutes

CET – 1990

Quantitative

55

1

120

44

3

9

55

Verbal

55

1

3

16

Analytical

55

1

2

12

CET – 1991

Quantitative

50

1

120

48

2

14

68

Verbal

50

1

1

19

Analytical

50

1

1

20

CET – 1992

Quantitative

50

1

120

48

3

11

65

Verbal

50

1

1

18

Analytical

50

1

3

14

CET – 1993

Quantitative

50

1

120

48

3

10

60

Verbal

50

1

1

18

Analytical

50

1

2

15

CET – 1994

Quantitative

37

1

150

71

3

8

68

Verbal

50

1

1

18

Analytical

39

1

3

9

 

* The Difficulty Factor of the exam is the sum of the products of the number of questions of each type and the corresponding difficulty level. The Stress Factor is the Difficulty Factor divided by the Average Time Per Question.

Question-1: (Medium Difficulty Level)

Indicate in the respective columns which of the following years can be marked as having the greatest Difficulty Factor and the Highest Stress Factor?
 
The Difficulty Factor is the greatest for which one of the following exams? Which one of the following exams has been marked as having the highest Stress Factor?  
CET 1990
CET 1991
CET 1992
CET 1993
CET 1994
 
Column I: The Difficulty Factor of the exam is the sum of the products of the number of questions of each type and the corresponding difficulty level.
 
Let’s calculate the Difficulty Factor for each exam and pick the answer-choice that has the greatest value:
 
Analysis of the first part (Column 1):
 
Row 1: In CET 1990, the Difficulty Factor is (3 × 55 + 3 × 55 + 2 × 55) = 165 + 165 + 110 = 440.
 
Row 2: In CET 1991, the Difficulty Factor is (2 × 50 + 1 × 50 + 1 × 50) = 100 + 50 + 50 = 200 < Row 1. Reject the current choice.
 
Row 3: In CET 1992, the Difficulty Factor is (3 50 + 1 × 50 + 3 × 50) = 350 < Row 1. Reject the current choice.
 
Row 4: In CET 1993, the Difficulty Factor is (3 × 50 + 1 × 50 + 2 × 50) = 300 < Row 1. Reject the current choice.
 
Row 5: In CET 1994, the Difficulty Factor is (3 × 37 + 1 × 50 + 3 × 39) = 111 + 50 + 117 = 278 < Row 1. Reject the current choice.
 
The greatest choice is Row 1. Choose it.
 
Analysis of the first part (Column 2):
 
Column II: Which one of the following exams has been marked as having the highest Stress Factor?
 
The Difficulty Factor of the exam is the sum of the products of the number of questions of each type and the corresponding difficulty level.
 
Then
 
The Stress Factor = (the Difficulty Factor) divided by (the average time per question).
 
Let’s calculate the Stress Factor for each answer-choice and choose the one that has the highest value:
 
Choice (A): In CET 1990,
The Difficulty Factor is (3 × 55 + 3 × 55 + 2 × 55) = 165 + 165 + 110 = 440
The Stress Factor is 440/44 = 10.
 
Choice (B): In CET 1991,
Difficulty Factor is (2 × 50 + 1 × 50 + 1 × 50) = 100 + 50 + 50 = 200.
The Stress Factor is 200/48 < Choice (A). Reject.

Choice (C): In CET 1992,
Difficulty Factor is (3 × 50 + 1 × 50 + 3 × 50) = 350.
The Stress Factor is 350/48 < Choice (A). Reject.

 

Choice (D): In CET 1993,
Difficulty Factor is (3 × 50 + 1 × 50 + 2 × 50) = 300.
The Stress Factor is 300/48 < Choice (A). Reject.

Choice (E): In CET 1994,
Difficulty Factor is (3 × 37 + 1 × 50 + 3 × 39) = 111 + 50 + 117 = 278.
The Stress Factor is 278/71 < Choice (A). Reject.
 
Hence, the answer is Row 1 and should be marked as follows:
 
The Difficulty Factor is the greatest for which one of the following exams? Which one of the following exams has been marked as having the highest Stress Factor?  
CET 1990
CET 1991
CET 1992
CET 1993
CET 1994

Question-2: (Hard Difficulty Level)

Which of the following statements can be inferred from the tables?
 
Enough to infer and true Note enough to infer or false  
As the Stress Factor increased, the cut-off marks of the top five universities decreased
As the Difficulty Factor of the exam decreased, the cut-off marks of the top five universities increased
As the Difficulty Factor increased, the Stress Factor increased
By approximately what percent did the number of questions decrease in CET 1994 over the previous year?
 
The increasing order of the Difficulty Factor is
 
CET 1991 (200) < CET 1994 (278) < CET 1993 (300) < CET 1992 (350) < CET 1990 (440)
 
The increasing order of the Stress Factor is
 
CET 1994 (278/71 = 3.92) < CET 1991 (200/48 = 4.16) < CET 1993(300/48 = 6.25) < CET 1992(350/48 = 7.29) < CET 1990 (440/44 = 10)
 
The decreasing order of the cut-off marks is
 
CET 1994 (68) > CET 1991 (65) > CET 1993 (60) > CET 1992 (58) > CET 1990 (55)
 
The decreasing order of the cut-off marks matches the increasing order of the Stress Factor. Hence, the statement in the Row I is true.
 
The decreasing order of the cut-off marks does not match the increasing order of the Difficulty Factor.
 
As the Difficulty Factor increased, the Stress Factor did not increase. Hence, the third statement is false, and we choose Column II (not enough or false) corresponding to Column II.
 
CET 1993 asks 50 quantitative, 50 verbal, and 50 Analytical.
 
The total is 50 + 50 + 50 = 150.
 
CET 1994 asks 37 quantitative, 50 verbal, and 39 Analytical.
 
The total is 37 + 50 + 39 = 126.
 
The decrease percent is

 

Hence, the answer should be marked as follows:
 
Enough to infer and true Note enough to infer or false  
As the Stress Factor increased, the cut-off marks of the top five universities decreased
As the Difficulty Factor of the exam decreased, the cut-off marks of the top five universities increased
As the Difficulty Factor increased, the Stress Factor increased
By approximately what percent did the number of questions decrease in CET 1994 over the previous year?




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