Statistics

high importance~3 Q in Tier 120 formulas⚡ 10 shortcuts5 subtopics

Overview Learn (5)Formulas (20)Examples (5)Practice (68)

Mean, median, mode and simple dispersion: raw-data medians, the mode = 3·median − 2·mean relation, grouped-data formulas, range and SD with shift-scale effects. Every question is formula-driven with small numbers — statistics is among the most scoring blocks in the Quant paper once the six formulas above are memorised.

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Learn — 5 subtopics

One page per subtopic: detailed notes, every question type, formulas, tricks and practice sets.

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Formula sheet

Every formula on one printable page, grouped by subtopic.

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Solved examples

5 exam-level questions worked step by step.

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Practice & test

68 questions — untimed practice or a timed test with analysis.

Track record in the exam

avg 1.0 Q / shift2024: 1 Q2025: 1 Q

Questions per shift in recent SSC CGL papers.

Test difficulty mix (68 questions)

24 easy30 medium14 hard

Question patterns exams keep repeating

Taken from previous-year papers. If a pattern is marked "very common", expect to see it in your exam.

Combined average of two groups

very common

Spot it:

Two classes/teams/genders with different sizes and averages merge into one.

How to solve: Weighted mean $\frac{n_1\bar{x}_1 + n_2\bar{x}_2}{n_1+n_2}$ ; equal sizes → plain average of the means.

Example: 30 boys average 62 kg and 20 girls average 58 kg. The class average is:

$\frac{30 \times 62 + 20 \times 58}{50} = 60.4$ kg.

Learn this in “Mean, weighted mean and combined mean” →

Member joins / leaves / replaced

very common

Spot it:

A new batsman, teacher or watch changes the group average by a stated amount.

How to solve: Work in totals: newcomer $= b + n(b-a)$ ; leaver $= a + n(a-b)$ ; replacement carries $n \times$ the shift.

Example: 24 students average 35 kg; with the teacher it rises 0.5 kg. The teacher's weight is:

$35 + 25 \times 0.5 = 47.5$ kg.

Learn this in “Mean, weighted mean and combined mean” →

Empirical 3M relation

very common

Spot it:

Two of mean/median/mode given (often clean integers), the third asked.

How to solve: $\text{mode} = 3\,\text{median} - 2\,\text{mean}$ ; rearrange for whichever is missing.

Example: Median 32, mean 30. The mode is:

$3 \times 32 - 2 \times 30 = 36$ .

Learn this in “Median and mode of raw data” →

Median/mode of grouped data

common

Spot it:

A frequency table with class intervals; sometimes a missing frequency to solve for.

How to solve: cf column → median class → $L + \frac{n/2 - cf}{f}h$ ; tallest frequency → mode formula.

Example: Frequencies 4, 6, 10, 8, 2 over classes 0-10...40-50. The median is:

$20 + \frac{15-10}{10} \times 10 = 25$ .

Learn this in “Median and mode of grouped data” →

Effect of scaling on mean and SD

common

Spot it:

'Each value is multiplied/divided and then shifted; find the new mean/SD/median.'

How to solve: Mean and median scale by $a$ then shift by $b$ ; SD only scales by $|a|$ — the shift never enters.

Example: SD is 7; each value is tripled and 5 added. The new SD is:

$3 \times 7 = 21$ .

Learn this in “Range, variance and standard deviation” →

Averages of consecutive / special series

common

Spot it:

First n naturals/squares/cubes, consecutive odds/evens, AP terms.

How to solve: AP → middle term; squares/cubes → closed-form sums ÷ n; cubes sum = (naturals sum)².

Example: The mean of the squares of the first 10 naturals is:

$\frac{11 \times 21}{6} = 38.5$ .

Learn this in “Averages of special series” →

Raise-the-average / innings problems

common

Spot it:

'How many runs in the next innings to raise the average to X?'

How to solve: Needed = new total − old total $= (n+1)X - n\bar{x}$ , i.e. $X + n(X - \bar{x})$ .

Example: Averaging 45 over 8 innings; score in the 9th to average 50:

$450 - 360 = 90$ .

Learn this in “Mean, weighted mean and combined mean” →

Misrecorded value corrections

occasional

Spot it:

A value was wrongly recorded; the corrected mean (or SD) asked.

How to solve: Correct the total by (true − recorded); mean shifts by $\frac{\text{error}}{n}$ . For SD, correct $\sum x^2$ too.

Example: Average of 30 results was 20; 24 was recorded as 21. The corrected average is:

$\frac{600 + 3}{30} = 20.1$ .

Learn this in “Mean, weighted mean and combined mean” →

Your next step

New here? Start with subtopic 1 in Learn. Revision mode? Jump straight to the test and let it tell you what to fix.