In this guide
The RRB NTPC Maths syllabus includes elementary statistics, and papers sometimes include a small table or chart with a few questions on it. These questions test two things: knowing the definitions exactly, and reading the data carefully. The arithmetic is usually percentages, ratios and averages that you already know.
Most marks lost here are lost to misreading, not to hard maths. So this guide gives you a reading routine as well as the formulas.
Mean, median, mode and range
| Measure | Meaning | How to find it |
|---|---|---|
| Mean | The average | Sum ÷ number of values |
| Median | The middle value | Arrange in order; take the middle value, or the mean of the two middle values for an even count |
| Mode | The most frequent value | The value that appears most often |
| Range | The spread | Largest − smallest |
Why the median needs sorting: it is defined by position in order. The third number as written means nothing; the third number after sorting is the middle.
For n values in order, the median is at position (n + 1) ÷ 2. For n = 5 that is the 3rd value; for n = 6 it falls between the 3rd and 4th, so you average those two.
Mean from a frequency table
When values repeat, multiply each value by its frequency, add, and divide by the total frequency.
| Marks (x) | 10 | 20 | 30 | 40 |
|---|---|---|---|---|
| Students (f) | 2 | 3 | 4 | 1 |
Mean = (20 + 60 + 120 + 40) ÷ 10 = 240 ÷ 10 = 24.
Median: 10 values, so average the 5th and 6th. Running totals are 2, 5, 9, 10, so the 5th is 20 and the 6th is 30. Median = 25.
Mode = 30 (highest frequency).
Weighted mean: combining groups
The combined mean of two groups is not the average of their means unless the groups are the same size.
Combined mean = (n₁ × mean₁ + n₂ × mean₂) ÷ (n₁ + n₂).
Why: the mean is a total spread evenly. Rebuild each group's total, add them, and spread the combined total over everyone.
Reading a table or chart: a routine
- Read the title and the units (numbers, thousands, lakh, percentages).
- Read the question and underline the rows, columns and years it asks about.
- Pull out only the numbers you need, and write them down.
- Calculate, then compare with the options. Approximate first if the options are far apart.
Percentage change = (new − old) ÷ old × 100. The base is always the earlier or reference value.
"A as a percentage of B" = A ÷ B × 100. The value after "of" goes underneath.
Practice table A: tickets sold
The figures below are made up for practice. They are not real data.
Tickets sold at a station (in thousands)
| Month | Reserved | Unreserved | Total |
|---|---|---|---|
| January | 40 | 60 | 100 |
| February | 45 | 75 | 120 |
| March | 50 | 80 | 130 |
| April | 42 | 48 | 90 |
| May | 48 | 102 | 150 |
Worked questions:
- Average reserved tickets per month? (40 + 45 + 50 + 42 + 48) ÷ 5 = 225 ÷ 5 = 45 thousand.
- Percentage increase in total tickets from April to May? (150 − 90) ÷ 90 × 100 = 66⅔%.
- Ratio of reserved to unreserved in February? 45 : 75 = 3 : 5.
- In which month was the reserved share of the total highest? January 40%, February 37.5%, March about 38.5%, April about 46.7%, May 32%. April.
- By what percentage were unreserved tickets in May more than in January? (102 − 60) ÷ 60 × 100 = 70%.
- Median of the monthly totals? In order: 90, 100, 120, 130, 150. Median = 120 thousand.
Practice table B: a percentage breakdown
Pie-chart questions often give a percentage breakdown. Made-up data again.
Monthly spending of a household (total ₹40,000)
| Head | Share |
|---|---|
| Food | 30% |
| Rent | 25% |
| Education | 15% |
| Transport | 10% |
| Savings | 20% |
Worked questions:
- Amount spent on food? 30% of 40,000 = ₹12,000.
- How much more on education than on transport? 5% of 40,000 = ₹2,000.
- Central angle for rent in a pie chart? 25% of 360° = 90°.
- Ratio of savings to food? 20 : 30 = 2 : 3.
Why work in percentages first: differences and ratios between heads can be taken straight from the percentages. Convert to rupees only once, at the end.
Common mistakes
- Not sorting before finding the median.
- Using the wrong base for percentage change. The base is the earlier value.
- Missing the units, such as "in thousands" or "in ₹ lakh".
- Averaging two group means without weighting by group size.
- Reading the wrong row or column. Put a finger or the cursor on the row before copying the number.
Practice set
- Find the mean of 12, 15, 18, 20 and 25.
- Find the median of 3, 8, 5, 10 and 7.
- Find the mode of 2, 4, 4, 6, 6, 6 and 8.
- Find the range of 14, 3, 22, 9 and 17.
- From table A, find total tickets sold from January to March.
- From table A, express April's unreserved tickets as a percentage of February's.
- From table B, if the income rises to ₹50,000 with the same percentages, how much more is spent on food?
- Class A has 30 students with an average of 60 marks, and class B has 20 students with an average of 70. Find the combined average.
Answers:
- 18. 90 ÷ 5.
- 7. Sorted: 3, 5, 7, 8, 10.
- 6. It appears three times.
- 19. 22 − 3.
- 350 thousand. 100 + 120 + 130.
- 64%. 48 ÷ 75 × 100.
- ₹3,000. 30% of the ₹10,000 rise.
- 64. (1,800 + 1,400) ÷ 50.
What to do next
- Solve 10 mean, median and mode questions, sorting the data every time before finding the median.
- Practise five table sets and five percentage-breakdown sets, following the four-step reading routine.
- Keep a list of every misreading you make in mocks. It is usually the same two or three habits.
- For Maths revision across the syllabus, go back to the NTPC Maths plan.
A note on dates and numbers. Exam patterns, vacancies and schedules change from year to year. Always confirm the current details in the latest notification on the Railway Recruitment Boards website .
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