Tables – Quantitative Aptitude Study Notes
(JNU Entrance – Quantitative Aptitude)
1. What are “Tables” in Aptitude?
| Term | Simple Explanation |
|---|---|
| Data/Value Table | A grid of numbers arranged in rows (x‑axis) and columns (y‑axis). The intersection (cell) gives the value of a function or a measurement. |
| Frequency Table | Shows how many times each value (or class) occurs in a data set. |
| Cumulative Frequency Table | Each cell contains the total of all frequencies up to that class. |
| Contingency Table | Cross‑tabulation of two categorical variables (e.g., gender × choice). |
| Interpolation Table | A table used to estimate missing values by linear interpolation. |
Why Tables Matter
They compress large amounts of data into a compact form and allow quick visual estimation of values, averages, percentiles, etc.
2. Key Concepts & Formulas
| Concept | Formula / Method | When to Use |
|---|---|---|
| Mean (Average) | (\displaystyle \bar{x} = \frac{\sum f_i x_i}{\sum f_i}) | Weighted mean from a frequency table |
| Median | Locate the 50 % point (or middle value) in the cumulative frequency distribution | Find the class where cumulative frequency ≥ ½ of total |
| Mode | Class with the highest frequency | Identify the most frequent class |
| Percentile | Find the class where cumulative frequency ≥ (p%) of total | e.g., 70th percentile |
| Linear Interpolation | (y = y_1 + \frac{(x - x_1)(y_2 - y_1)}{x_2 - x_1}) | Estimate missing values in a value table |
| Cumulative Frequency | (CF_i = \sum_{k=1}^{i} f_k) | Needed for median, percentile |
| Relative Frequency | (\displaystyle RF_i = \frac{f_i}{N}) | Percentage representation |
| Proportion from Contingency Table | (\displaystyle \frac{\text{cell count}}{\text{total}} \times 100%) | Probability or percentage of a cell |
3. Types of Tables & How to Read Them
| Table Type | Typical Columns/Rows | How to Read |
|---|---|---|
| Value Table | X‑values (rows) × Y‑values (columns) | Find the row, then the column → the cell is the answer |
| Frequency Table | Class intervals × Frequency | Add frequencies → total. Use CF (cumulative frequency) to locate medians, percentiles |
| Cumulative Frequency Table | Classes × Cumulative Frequency | Directly gives the accumulated total up to that class |
| Contingency Table | Row variable × Column variable | Find total for row/column; compute percentages |
4. Common Problem Types
- Missing Value in a Value Table
Use linear interpolation or extrapolation. - Finding Mean, Median, Mode from Frequency Table
Use formulas above; remember to use CF for median. - Percentile Estimation
Locate the class in which the percentile falls. - Probability from Contingency Table
Divide cell count by grand total. - Data Compression
Use a cumulative table to answer “how many are above X?” quickly.
5. Worked Example
Problem
A student’s marks in 5 subjects are given in a value table. Find the subject in which the student scored <‑ 75.
| Subject | Mark |
|---|---|
| Math | 82 |
| Physics | 69 |
| Chemistry | 88 |
| Biology | 57 |
| English | 74 |
Answer: Biology
Why?
Scan the column of marks → the only value less than 75 is 57 (Biology).
A More Challenging Example
Data: Frequency distribution of scores (in multiples of 10) in a test.
| Score (≤) | Frequency |
|---|---|
| 10 | 2 |
| 20 | 5 |
| 30 | 9 |
| 40 | 12 |
| 50 | 8 |
| 60 | 4 |
| 70 | 1 |
-
Total students
(\displaystyle N = 2+5+9+12+8+4+1 = 41) -
Mean (average)
[ \bar{x} = \frac{(10)(2)+(20)(5)+(30)(9)+(40)(12)+(50)(8)+(60)(4)+(70)(1)}{41} ] [ = \frac{20+100+270+480+400+240+70}{41} = \frac{1660}{41}\approx 40.49 ] -
Median
Half of 41 → 20.5th observation.
Cumulative frequency:- 10: 2
- 20: 7
- 30: 16
- 40: 28 → median lies in the