Statistics
🔒 Log in to trackMean, 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.
One page per subtopic: detailed notes, every question type, formulas, tricks and practice sets.
Every formula on one printable page, grouped by subtopic.
5 exam-level questions worked step by step.
68 questions — untimed practice or a timed test with analysis.
Track record in the exam
Questions per shift in recent SSC CGL papers.
Test difficulty mix (68 questions)
Question patterns exams keep repeating
Taken from previous-year papers. If a pattern is marked "very common", expect to see it in your exam.
Average of two groups joined
very common"30 boys average 62 kg and 20 girls average 58 kg. Find the class average."
Find each group's total (number × average).
Add the totals and divide by all the people.
30 boys average 62 kg and 20 girls average 58 kg. Class average?
Boys' total = 30 × 62 = 1860
Girls' total = 20 × 58 = 1160
All together = 3020 for 50 students
3020 ÷ 50 = 60.4 kg
Someone joins or leaves the group
very common"With the teacher included, the average rises by 0.5 kg."
Work with totals, not averages.
The newcomer's value = new total − old total.
24 students average 35 kg. With the teacher, the average rises by 0.5 kg. Teacher's weight?
Students' total = 24 × 35 = 840
With teacher: 25 × 35.5 = 887.5
Teacher = 887.5 − 840 = 47.5 kg
Mean, median and mode together
very common"Median is 32 and mean is 30. Find the mode."
Mode = 3 × median − 2 × mean.
Rearrange if a different one is missing.
Median is 32 and mean is 30. Find the mode.
Mode = 3 × median − 2 × mean
= 3 × 32 − 2 × 30
= 96 − 60
Mode = 36
Median from a frequency table
commonA table of class intervals (0–10, 10–20, ...) with frequencies.
Add running totals until you pass half the total; that class holds the median.
Median = class start + (half − total before) ÷ frequency × class width.
Frequencies 4, 6, 10, 8, 2 for classes 0–10, 10–20, 20–30, 30–40, 40–50. Find the median.
Total = 30, half = 15
Running totals: 4, 10, 20, so the median class is 20–30
Before it: 10 students; in it: 10 students
Median = 20 + (15 − 10) ÷ 10 × 10 = 25
Every value is changed the same way
common"Each value is tripled and 5 is added. Find the new SD."
Multiplying changes both the average and the spread.
Adding only moves the average; the spread stays the same.
SD is 7. Each value is tripled and then 5 is added. New SD?
Tripling makes the spread 3 times: 3 × 7 = 21
Adding 5 slides every value, so the spread is unchanged
New SD = 21
Average of a number series
common"Find the mean of the squares of the first 10 natural numbers."
Use the sum formula for the series, then divide by how many terms.
For evenly spaced numbers, the average is the middle value.
Mean of the squares of the first 10 natural numbers?
Sum of squares 1 to n = n × (n + 1) × (2n + 1) ÷ 6
For n = 10: 10 × 11 × 21 ÷ 6 = 385
Mean = 385 ÷ 10 = 38.5
Runs needed to lift the average
common"How many runs in the next innings to make the average 50?"
Find the total needed after the next innings.
Subtract the total so far.
A batsman averages 45 over 8 innings. What must he score in the 9th to average 50?
Runs so far = 8 × 45 = 360
Needed after 9 innings = 9 × 50 = 450
Score in the 9th = 450 − 360 = 90
One value was written wrongly
occasional"24 was wrongly recorded as 21. Find the correct average."
Fix the total by adding or removing the mistake.
Then divide by the same number of items.
The average of 30 results was 20, but 24 was recorded as 21. Correct average?
Wrong total = 30 × 20 = 600
24 was written as 21, so 3 is missing
Correct total = 603
603 ÷ 30 = 20.1