Navy SSR – Quantitative Aptitude
Topic: Tables
Tables are a compact way of presenting data.
In the Navy SSR you’ll encounter frequency tables, cumulative tables, percentages, ratios, and data‑driven questions that require you to read, manipulate and infer values.
1. Simple Explanation
| Item | What it is | When it’s used |
|---|---|---|
| Frequency Table | Rows = categories, columns = frequency counts | Counting occurrences (e.g., number of recruits per month) |
| Cumulative Frequency Table | Adds frequencies progressively | Finding medians, percentiles |
| Percent Table | Shows percentages of a whole | Calculating proportions |
| Ratio Table | Shows two related quantities | Comparing rates (e.g., output per worker) |
| Gapped Table | One or more cells missing | Fill‑in‑the‑blank problems |
Key idea – Treat the table as a mini‑database.
Goal – Use the given numbers to deduce the unknowns, often by cross‑checking totals or percentages.
2. Key Points / Study Guide
| Category | How to Approach | Tips |
|---|---|---|
| Reading a Table | 1. Identify the header (what each column/row represents). 2. Locate totals (row/column sums). 3. Note any percentages or ratios given. |
Look for “TOTAL” or “SUM” rows/columns. |
| Finding Missing Numbers | 1. Use the sum or percentage information. 2. Convert percentages to fractions if needed. 3. Apply proportion or ratio formulas. |
Keep track of units (e.g., % = 1/100). |
| Calculating Mean / Median | - Mean: (∑ value × frequency) ÷ total frequency. - Median: Locate the middle cumulative frequency. |
For grouped data, use mid‑points of class intervals. |
| Working with Cumulative Tables | 1. Verify that cumulative values are non‑decreasing. 2. Subtract successive rows to get raw frequencies. |
Cumulative total equals overall total. |
| Using Percentages | If 40% of 200 = X, then X = 0.40 × 200 = 80. | Convert percentages to decimals before multiplying. |
| Ratios & Proportions | If A:B = 3:4 and A = 12, then B = (4/3) × 12 = 16. | Cross‑multiply to solve. |
3. Worked Example (Full Solution)
Problem
| Month | Recruits | % of Total |
|---|---|---|
| Jan | 120 | 20% |
| Feb | 160 | 26.7% |
| Mar | 200 | ? |
| Apr | 80 | 13.3% |
| Total | ? | 100% |
Find the number of recruits in March and the overall total recruits.
Step‑by‑Step
-
Calculate the Overall Total
The percentages for Jan, Feb, and Apr sum to:
(20 + 26.7 + 13.3 = 60%)
Therefore, the remaining percentage is (100 - 60 = 40%).Let T be the total recruits.
( \text{Jan} = 0.20T = 120 \Rightarrow T = 600) -
Verify with other months
- Feb: (0.267T = 0.267 \times 600 = 160.2 \approx 160) (rounded).
- Apr: (0.133T = 0.133 \times 600 = 79.8 \approx 80).
So the total recruits T = 600 (consistent).
-
Find March recruits
March’s percentage = (40%).
( \text{Mar} = 0.40 \times 600 = 240) -
Check the table
- Jan 120 + Feb 160 + Mar 240 + Apr 80 = 600 ✔️
- Percentages sum to 100% ✔️
Answer
- March recruits = 240
- Total recruits = 600
4. Quick Revision Summary
| Topic | Quick Tip |
|---|---|
| Missing Cell | Use total or percentage to compute. |
| Mean from Frequency Table | (\displaystyle \bar{x} = \frac{\sum f_i x_i}{\sum f_i}) |
| Median from Cumulative Table | Find the class where cumulative frequency ≥ ½ total. |
| Percentages | Convert % → decimal before multiplying. |
| Ratios | Cross‑multiply: (A:B = C:D \Rightarrow A \times D = B \times C). |
| Check Work | Verify totals (sum of rows/cols) and percentages add to 100%. |
| Common Mistakes | Forgetting to convert % to decimal; mixing up row/column totals; rounding errors. |
Practice Idea:
Create a 4‑row frequency table with one missing cell and a 10% gap.
Calculate the missing value and the overall mean.
Check your answer by summarizing the data in a single sentence.
Final Thought
Tables are tiny data sets that demand exact arithmetic and logical consistency.
Master the mechanics above,