In this guide
The RRB Group D maths syllabus includes elementary statistics. The questions are short: find a mean, a median or a mode, work backwards from a given mean, or read a few numbers from a table.
The trap is not difficulty. It is definitions. A candidate who forgets to sort the numbers before finding the median, or who reports the frequency instead of the value as the mode, loses a mark on a question that was meant to be free. This guide fixes those definitions and gives you a method for each type.
The four measures
| Measure | Meaning | How to find it |
|---|---|---|
| Mean | The average | Sum of values ÷ number of values |
| Median | The middle value | Sort the values. Odd count: the middle one. Even count: the average of the two middle ones |
| Mode | The most common value | The value that appears most often |
| Range | The spread | Largest value − smallest value |
For n values in order, the median is the ((n + 1) ÷ 2)th value when n is odd. When n is even, it is the average of the (n ÷ 2)th and the (n ÷ 2 + 1)th values.
Mean from a frequency table
When values repeat, the data may be given as a table of values (x) and how often each appears (f, the frequency).
- Mean = Σfx ÷ Σf, where Σ means "add them all up".
- Multiply each value by its frequency, add those products, then divide by the total frequency.
For the median of such a table, write the cumulative totals and find where the middle position falls.
What happens when every value changes
| Change to every value | Mean, median, mode | Range |
|---|---|---|
| Add or subtract k | Go up or down by k | No change |
| Multiply by k | Multiplied by k | Multiplied by k |
These make some questions one-line answers. If the mean of a set is 20 and every value is increased by 5, the new mean is 25. There is no need to find the values.
Worked examples
Example 1: Find the median of 9, 3, 7, 5, 11 and 1.
- Sort: 1, 3, 5, 7, 9, 11. There are six values, so take the 3rd and 4th: 5 and 7.
- Median = (5 + 7) ÷ 2 = 6.
Example 2: Find the mode and range of 4, 6, 6, 7, 7, 7, 9 and 12.
- 7 appears three times, more than any other value. Mode = 7.
- Range = 12 − 4 = 8.
Example 3: The mean of 6, 8, x, 12 and 14 is 10. Find x.
- Total = mean × count = 10 × 5 = 50.
- 6 + 8 + 12 + 14 = 40, so x = 50 − 40 = 10.
Example 4: Ten students scored these marks. Find the mean, median and mode.
| Marks (x) | 10 | 20 | 30 | 40 |
|---|---|---|---|---|
| Students (f) | 2 | 3 | 4 | 1 |
- Σfx = 10 × 2 + 20 × 3 + 30 × 4 + 40 × 1 = 20 + 60 + 120 + 40 = 240. Σf = 10.
- Mean = 240 ÷ 10 = 24.
- Median: there are 10 values, so take the 5th and 6th. The first 2 are 10s, the next 3 (3rd to 5th) are 20s, and the next 4 (6th to 9th) are 30s. So the median is (20 + 30) ÷ 2 = 25.
- Mode = 30, the value with the highest frequency.
Example 5: The mean of 5 numbers is 18. One number, 30, is removed. Find the new mean.
- Total = 5 × 18 = 90. After removing 30, the total is 60 for 4 numbers.
- New mean = 60 ÷ 4 = 15. This is the same "total" idea used in averages.
Reading a data table
The numbers below are made up for practice.
Notebooks sold by a shop
| Day | Notebooks |
|---|---|
| Monday | 30 |
| Tuesday | 45 |
| Wednesday | 25 |
| Thursday | 50 |
| Friday | 40 |
Example 6: From the table, find the total, the average per day, the rise from Monday to Tuesday, and the ratio of Wednesday to Thursday.
- Total: 30 + 45 + 25 + 50 + 40 = 190.
- Average per day: 190 ÷ 5 = 38.
- Rise from Monday to Tuesday: 15 ÷ 30 × 100 = 50%.
- Wednesday : Thursday = 25 : 50 = 1 : 2.
Common mistakes
- Finding the median without sorting the values first.
- Taking one middle value when the count is even.
- Reporting the frequency as the mode.
- In a frequency table, dividing Σfx by the number of different values instead of by Σf.
- Working out a percentage change on the new value instead of the original one.
Practice set
- Find the mean of 2, 4, 6, 8 and 10.
- Find the median of 12, 7, 9, 15 and 10.
- Find the mode of 3, 5, 5, 8, 8, 8 and 9.
- Find the median of 3, 8, 1, 6, 10 and 4.
- From the notebook table, on which day were the most notebooks sold?
- From the notebook table, Friday's sales are what percentage of Thursday's?
- The mean of 4, 5 and 9 is 6. If 6 is added to each number, what is the new mean?
- The range of a set is 15. If every value is doubled, what is the new range?
Answers:
- 6. 30 ÷ 5.
- 10. Sorted: 7, 9, 10, 12, 15. The middle (3rd) value is 10.
- 8. It appears three times.
- 5. Sorted: 1, 3, 4, 6, 8, 10. (4 + 6) ÷ 2.
- Thursday, with 50.
- 80%. 40 ÷ 50 × 100.
- 12. Adding 6 to every value adds 6 to the mean.
- 30. Multiplying every value by 2 doubles the range.
What to do next
- Write the four definitions and the median rule for odd and even counts on your formula card.
- Solve ten questions that work backwards from a mean, like Example 3.
- Practise two small data tables a day for a week, answering total, average, percentage and ratio for each.
- Revise percentage and ratio, which most table questions use.
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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