📚 Quantitative Aptitude – Tables
(Advanced, MIT‑Level Study Notes for Gujarat Police Sub‑Inspector Exams)
Table – a systematic arrangement of data in rows and columns that facilitates quick reference, comparison, and analysis.
In aptitude, tables are used to solve problems of proportion, percentages, probability, statistics, and more.
Table of Contents
| Section | Topics |
|---|---|
| 1 | What is a Table? |
| 2 | Types of Tables |
| 3 | Constructing a Table (From Raw Data) |
| 4 | Interpreting a Table |
| 5 | Common Problem Types |
| 6 | Advanced Theory & Edge Cases |
| 7 | Challenging Problem (MIT‑Level) |
| 8 | Summary & Quick Tips |
1. What is a Table?
| Feature | Description |
|---|---|
| Rows | Distinct categories or observations |
| Columns | Quantitative or qualitative attributes |
| Cells | Numerical values (counts, percentages, frequencies, etc.) |
| Purpose | Summarise data compactly; enable comparison and inference |
Key Idea: A well‑structured table is a data compression tool – it reduces long lists to a few cells, while preserving all essential information.
2. Types of Tables
| Table | Definition | Typical Use | Example |
|---|---|---|---|
| Frequency Table | Counts of occurrences in each category. | Basic data summarisation. | `Sex |
| Cumulative Frequency Table | Running total of frequencies. | Determine medians, percentiles. | `Score |
| Percentage Table | Frequency expressed as a percent of total. | Quick comparison of proportions. | `Country |
| Contingency Table | Cross‑tabulation of two categorical variables. | Association tests (Chi‑square). | Gender × Pass/Fail |
| Probability Table | Probabilities of discrete events. | Probability calculations. | `Coin Toss |
| Statistical Table | Mean, median, mode, variance, SD. | Descriptive stats. | `Age |
| Interpolation Table | Values estimated between known data points. | Linear interpolation. | `Temperature |
Rule of Thumb: Start with a frequency table; then transform into others as needed.
3. Constructing a Table (From Raw Data)
-
Identify Variables
- Qualitative (categories) → rows
- Quantitative (values) → columns
-
Choose a Suitable Table Type
- Frequency → count occurrences
- Cumulative → add successive frequencies
-
Set Up Headers
- Clear, unambiguous labels.
- Include units if applicable.
-
Tally Observations
- Use a tally sheet or spreadsheet.
-
Fill in Cells
- Count, sum, or compute as required.
-
Validate Totals
- Sum of rows = column totals = grand total.
Example: 5‑Day Sales Data
| Day | Units Sold | Revenue (₹) |
|---|---|---|
| Mon | 120 | 4,800 |
| Tue | 95 | 3,800 |
| Wed | 110 | 4,400 |
| Thu | 130 | 5,200 |
| Fri | 90 | 3,600 |
| Total | 545 | 21,200 |
Tip: Use a spreadsheet for large data sets; it automatically checks sums.
4. Interpreting a Table
| Question | How to Answer |
|---|---|
| What is the total count? | Sum column/row. |
| What is the percentage of a category? | (frequency / grand total) × 100. |
| What is the median? | Find the cumulative frequency that crosses ½ of the grand total. |
| What is the mode? | Category with highest frequency. |
| What is the mean? | (Sum of (value × frequency)) / grand total. |
| What is the standard deviation? | Use σ = sqrt(Σ(f × (x - μ)²) / N). |
Edge Cases:
- Zero frequency → can't compute ratios → treat as missing or suppressed.
- Negative values → usually invalid for counts; check data source.
5. Common Problem Types
-
Missing Values
- Given: Total and all but one frequency → compute missing one.
- Solution:
Missing = Grand Total – Σ(known frequencies).
-
Percentage Change
- Given: Old and new values → compute percent change.
-
Cumulative Frequency for Percentiles
- Given: Table → find percentile rank of a value.
-
Contingency Table Analysis
- Given: Two categorical variables → compute conditional probabilities.
-
Probability Tables
- Compute: Expected value, variance.