Tables, Matrices and Structured Data Notes for CAT: Concepts, Formulas, Worked Examples & Practice

Tables, Matrices and Structured Data notes for CAT: 40 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

Chapter Roadmap: Tables, Matrices and Structured Data

Chapter Roadmap

1. Rating Tables and Score Matrices

High Weightage. Master integer reconstruction and cumulative averages.

2. Nutrition and Composition Tables

Moderate. Focus on percentage changes and mixture logic in grids.

3. Grid Matrices and Box Arrays

Moderate. Spatial logic, coin distributions, and 2D constraints.

4. Pandemic and Mortality Data Tables

Highest Weightage. Time-series data, rates, and overlapping conditions.

By the end of this chapter, you will be able to look at any structured data set, extract the hidden sums using averages, and reconstruct missing cells using integer constraints and logical bounds.

The Anatomy of a Rating Matrix

A rating table is a structured grid where:

Rows represent entities (e.g., Days, Restaurants, Products).

Columns represent categories (e.g., Rating scale 1 to 5, or specific Workers).

Cells contain either the count of ratings or the actual integer scores.

The Core Challenge

You are never asked to do complex arithmetic. You are asked to translate. You will be given summary statistics and must reverse-engineer the exact integer values hidden inside the grid.

The Golden Rule

Every summary statistic is just a disguised equation for the sum of that row or column.

The Core Engine: Summary Statistics as Equations

Summary Statistics as Equations

Mean

Sum=Mean×Count

The most powerful tool. Converts an average into a hard integer sum.

Median

The middle value when sorted. For

N

items, it is the

\frac{N + 1}{2}

-th item.

Splits the data into two halves.

Mode

The most frequent value.

If the mode is

x

, you must place at least two

x

's in the row or column.

Range

Max−Min

Locks the boundaries. If Min is 1 and Range is 4, Max is strictly 5.

The Cumulative Average Mechanics

Cumulative Average Mechanics

Cumulative Average is the average of all data points collected up to that moment.

Cumulative Average at Day N = \frac{Total Sum up to Day N}{Total Count up to Day N}

Daily Average

Uses only that day's data.

Cumulative Average

Uses all previous days + today.

Finding a specific day's sum:

Today’s Sum = (Today’s Cum Avg \times Total Count) - (Yesterday’s Cum Avg \times Yesterday’s Count)

Tables, Matrices and Structured Data: Solved Questions with Step-by-Step Explanations (2 Problems)

Question 1 · Data Interpretation and Logical Reasoning MCQ

In a restaurant rating matrix, if the summary statistics state that the "modal rating" for a specific worker is 4, what does this definitively mean?

A.
The rating of 4 was given to this worker more frequently than any other rating.
B.
The worker received a rating of 4 from every single restaurant.
C.
The middle rating when all ratings are sorted is 4.
D.
The difference between the highest and lowest rating is 4.

Correct Answer:

Step-by-Step Solution

Key idea: This is a direct definition check for "Mode" in the context of rating data, recognisable because it asks for the meaning of a specific summary statistic.

Step 1: Recall the definition of Mode.

The mode is the value that appears most frequently in a dataset.

Step 2: Apply to the context.

A "modal rating" of 4 means the number 4 appears more times than 1, 2, 3, or 5 in that worker's set of ratings.

Step 3: Evaluate the options.

Option A matches the definition of mode perfectly. Option B describes a constant rating, Option C describes the median, and Option D describes the range.

Answer: A

Question 2 · Data Interpretation and Logical Reasoning MCQ

In a grid matrix, a specific box contains $n$ sub-items. If the average value of these sub-items is $A$ , which of the following formulas correctly calculates the total sum of the sub-items in that box?

A.
$A + n$
B.
$A - n$
C.
$A im es n$
D.
$A / n$

Correct Answer:

Step-by-Step Solution

Key idea: This is a foundational translation question, recognisable because it asks for the mathematical relationship between a cell's average, its count, and its total sum.

Step 1: Recall the definition of an average.

$Average = \frac{Total Sum}{Count}$

Step 2: Rearrange the formula to solve for the Total Sum.

$Total Sum = Average \times Count$

Step 3: Substitute the given variables.

$Total Sum = A \times n$

Answer: C

More notes in this unit

chapter

Tables, Matrices and Structured Data Notes for CAT: Concepts, Formulas, Worked Examples & Practice

Tables, Matrices and Structured Data notes for CAT: 40 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

A question from this chapter

Question 1

In a restaurant rating matrix, if the summary statistics state that the "modal rating" for a specific worker is 4, what does this definitively mean?

Question 2

In a grid matrix, a specific box contains n sub-items. If the average value of these sub-items is A, which of the following formulas correctly calculates the total sum of the sub-items in that box?

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