📊 Tables – Delhi TET (Quantitative Aptitude)
Why tables matter?
In TET, tables help you organise data, spot patterns and answer questions that involve frequency, mean, median, mode, and percentile calculations.
1. Simple Explanation
| Term | Definition | Quick Tip |
|---|---|---|
| Frequency Table | Counts of each distinct value in a data set. | Use “# of occurrences” column. |
| Relative Frequency | Frequency ÷ Total observations (often expressed as a percentage). | Handy for comparing categories of different sizes. |
| Cumulative Frequency | Running total of frequencies up to a given value. | Helps find medians, percentiles quickly. |
| Continuous Data Table | Data grouped into class intervals (e.g., 0‑5, 6‑10). | Use mid‑point for calculations. |
| Discrete Data Table | Exact values (e.g., 1, 2, 3). | Each value is its own class. |
Key Idea: Tables convert a messy list of numbers into a clear, visual structure that lets you answer questions in seconds.
2. Key Points to Remember
| Category | Points |
|---|---|
| Creating a Frequency Table | 1. List all distinct values (ascending). 2. Count occurrences. 3. Add a “Total” row. |
| Relative Frequency | Relative Frequency = Frequency / Total Express as a fraction or % (multiply by 100). |
| Cumulative Frequency | Add each frequency to the sum of all previous frequencies. Useful for locating the median or a given percentile. |
| Mean from a Frequency Table | Mean = Σ (value × frequency) / Total |
| Median & Mode | • Mode: value with highest frequency. • Median: Find the position n/2 (or (n/2)+1 for even n) in the cumulative frequency. |
| Mode for Continuous Data | Use the class with the highest frequency. |
| Percentile (P) | Find the class where the cumulative frequency ≥ P% of total. |
| Skewness | Roughly: If the mean > median → right‑skewed; if mean < median → left‑skewed. |
| Typical TET Questions | • Find mean, median, mode. • Compute relative frequency, cumulative frequency. • Identify the 75th percentile. • Compare two data sets using tables. |
3. Worked Example
Problem (Delhi TET style)
A class of 30 students took a test. Their scores (out of 100) are:
45, 52, 45, 67, 58, 60, 45, 70, 65, 60, 45, 55, 70, 80, 65, 70, 55, 60, 58, 70, 67, 55, 45, 60, 70, 65, 80, 65, 60, 55.
Tasks
- Construct a frequency table.
- Find the mean, median, and mode.
- Compute the relative frequency (as a percentage).
- Find the cumulative frequency.
- Locate the 75th percentile score.
Step 1 – Frequency Table
| Score | Frequency |
|---|---|
| 45 | 5 |
| 52 | 1 |
| 55 | 4 |
| 58 | 2 |
| 60 | 5 |
| 65 | 4 |
| 67 | 2 |
| 70 | 5 |
| 80 | 2 |
| Total | 30 |
Step 2 – Mean
Mean = Σ(score × frequency) / Total
= (45×5 + 52×1 + 55×4 + 58×2 + 60×5 + 65×4 + 67×2 + 70×5 + 80×2) / 30
= (225 + 52 + 220 + 116 + 300 + 260 + 134 + 350 + 160) / 30
= 1,797 / 30
= 59.9
Mean ≈ 59.9
Step 3 – Median
n = 30 (even), so median position = n/2 = 15th value.
We need cumulative frequency:
| Score | Frequency | Cumulative |
|---|---|---|
| 45 | 5 | 5 |
| 52 | 1 | 6 |
| 55 | 4 | 10 |
| 58 | 2 | 12 |
| 60 | 5 | 17 |
| 65 | 4 | 21 |
| 67 | 2 | 23 |
| 70 | 5 | 28 |
| 80 | 2 | 30 |
The 15th student falls in the 60 score group (cumulative 17).
Median = 60
Step 4 – Mode
Highest frequency is 5 (scores 45, 60, 70).
Mode = 45, 60, 70 (triple mode).
Step 5 – Relative Frequency (%)
Relative Frequency of 45 = 5/30 × 100 = 16.67%
Similarly:
52: 3.33%
55: 13.33%
58: 6.67%
60: 16.67%
65: 13.33%
67: 6.67%
70: 16.67%
80: 6.67%
Step 6 – 75th Percentile
75% of 30 = 22.5 → look for cumulative ≥ 23.
Cumulative at 70 is 28, which is ≥ 23, so the 75th percentile score is 70.
Summary Table
| Attribute | Value |
|---|---|
| Mean | 59.9 |
| Median |