Elementary Statistics — RRB NTPC Mathematics
This topic carries roughly 5% of Mathematics's 30 questions, and stays limited to the four basic measures: mean, median, mode, and range, applied to small, direct data sets.
1. What RRB NTPC actually asks
Expect direct mean/median/mode/range calculations on a small data set, and word problems where a value is replaced, added, or removed and the new mean/average must be found.
2. The four core measures
Mean = sum of all values ÷ number of values.
Median = the middle value when data is arranged in order. For an even count, it's the average of the two middle values.
Mode = the value that occurs most frequently in the data set.
Range = highest value − lowest value.
3. Sum-based shortcut for "replace/add a value" problems
Rather than recomputing the full average from scratch, use the sum directly: new sum = old sum − removed value + added value (or just + added value if nothing was removed), then divide by the (possibly changed) count.
Worked examples
Q1. The mean of 5 numbers is 18. If one number is removed, the mean of the remaining 4 numbers becomes 16. What was the removed number?
Pick an option to check your answer.
Show explanation
Solution. Sum of original 5 numbers = 5 × 18 = 90. Sum of remaining 4 numbers = 4 × 16 = 64.
Removed number = 90 − 64 = 26. Answer: (c).
Q2. The average age of 30 students in a class is 12 years. When the class teacher's age is included, the average becomes 13 years. What is the teacher's age?
Pick an option to check your answer.
Show explanation
Solution. Total age of 30 students = 30 × 12 = 360. Total age including the teacher (31 people) = 31 × 13 = 403.
Teacher's age = 403 − 360 = 43. A common error is dividing by 30 instead of 31 for the new total, or forgetting the count itself increases by one when the teacher joins. Answer: (c).
5. Common traps
- Forgetting the count changes when a value is added or removed — always recompute using the correct new count, not the original one.
- Confusing median with mean. Median is the positional middle value; mean is the arithmetic average — they're often different for the same data set.
- Sorting the data before finding the median. Median requires the data in ascending (or descending) order — a common error is reading off the "middle" of an unsorted list.
- Missing that mode can have more than one value (bimodal) or none at all (if all values are unique) — RRB NTPC questions typically avoid this ambiguity, but it's worth checking the data carefully.
6. Guessing strategy
For "find the removed/added value" problems, the sum-based shortcut (new sum = old sum ± value) is always faster than trying to guess-and-check — compute directly rather than eliminating options.
Summary
- Elementary Statistics is roughly 5% of Mathematics's 30 CBT 1 questions, limited to mean, median, mode, and range.
- Mean = sum ÷ count; Median = middle value (average of two middles if count is even); Mode = most frequent value; Range = highest − lowest.
- For "replace/add/remove a value" problems, work directly with sums: new sum = old sum − removed + added.
- Always recompute using the correct (possibly changed) count after a value is added or removed.
- Median requires sorted data — never read off the middle of an unsorted list.
