In this guide
Statistics and probability are small parts of the SSC CGL maths syllabus, but they reward preparation disproportionately. The questions are usually direct — find the median of a list, the mean after a change, or the probability of drawing a king from a pack — and a few formulas cover almost all of them. For candidates aiming at Junior Statistical Officer, these topics are also the starting point for the separate Statistics paper.
Mean, median and mode
| Measure | Meaning | How to find it |
|---|---|---|
| Mean | Arithmetic average | Sum ÷ number of values |
| Median | Middle value in ordered data | For n values: the (n + 1)/2-th value if n is odd; the average of the two middle values if n is even |
| Mode | Most frequent value | The value that occurs most often |
Worked example: Find the median of 12, 7, 15, 9, 20, 11.
Ordered: 7, 9, 11, 12, 15, 20. n = 6, so median = (11 + 12)/2 = 11.5.
Empirical relation
For moderately skewed data: Mode = 3 Median − 2 Mean.
Worked example: If the mean is 30 and the median is 32, the mode ≈ 96 − 60 = 36.
Effect of changes on the mean
- Adding k to every value adds k to the mean (and to the median and mode).
- Multiplying every value by k multiplies the mean by k.
Worked example: The mean of 10 numbers is 25. If 4 is added to each, the new mean = 29. If each is doubled instead, the new mean = 50.
Grouped data (basics)
- Mean = Σfx/Σf, using class midpoints as x.
- Median class — the class where the cumulative frequency first reaches n/2.
- Modal class — the class with the highest frequency.
Dispersion
| Measure | Formula / meaning |
|---|---|
| Range | Largest − smallest |
| Variance | Average of squared deviations from the mean |
| Standard deviation (SD) | √variance |
- Adding a constant to every value does not change the SD.
- Multiplying every value by k multiplies the SD by |k| and the variance by k².
Worked example: Find the variance of 2, 4, 6, 8.
Mean = 5. Squared deviations: 9, 1, 1, 9 → sum 20. Variance = 20/4 = 5; SD = √5.
Probability
P(event) = favourable outcomes ÷ total outcomes, which always lies between 0 and 1.
P(not A) = 1 − P(A).
Coins
- One coin: P(head) = 1/2.
- Two coins: outcomes HH, HT, TH, TT. P(at least one head) = 3/4.
Dice
- One die: 6 outcomes. P(even) = 1/2.
- Two dice: 36 outcomes.
Worked example: Two dice are thrown. Find the probability that the sum is 8.
Favourable: (2,6), (3,5), (4,4), (5,3), (6,2) = 5. P = 5/36.
Playing cards
A standard pack has 52 cards: 4 suits of 13; 26 red and 26 black; 12 face cards (J, Q, K); 4 aces.
Worked example: One card is drawn. Find the probability that it is a king or a heart.
Kings = 4, hearts = 13, and the king of hearts is counted twice: 4 + 13 − 1 = 16. P = 16/52 = 4/13.
Balls in a bag
Worked example: A bag has 5 red and 3 blue balls. Two are drawn without replacement. Find the probability that both are red.
(5/8) × (4/7) = 5/14.
For JSO aspirants: Paper II
The Statistics paper goes much further — probability distributions, sampling, correlation and regression, index numbers, time series, statistical inference and more, at graduation level. Treat this post as a starting point and follow the Paper II syllabus in your notification.
Practice
- Find the mean of 3, 7, 8, 12, 15.
- Find the median of 21, 14, 8, 30, 17, 25, 11.
- If the median is 20 and the mean is 22, estimate the mode.
- The SD of a data set is 4. What is the SD if each value is multiplied by 3?
- Two coins are tossed. What is the probability of getting exactly one tail?
- A card is drawn from a pack of 52. What is the probability that it is a red face card?
Answers: 1. 9. 2. 17. 3. 16. 4. 12. 5. 1/2. 6. 3/26.
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 Staff Selection Commission website .
Get the next SSC CGL guide by email
New guides every week. No spam, unsubscribe any time.