Statistics basics
Statistics basics · mean · median · mode · variance
9 min read · Updated 2026-05-26
What is a measure of central tendency?
A measure of central tendency is a single number standing in for a whole set of data: the mean is the total divided by the count, the median the middle value of a sorted list and the mode the most frequent value. Spread is read from the range, the variance — the mean of squared deviations — and its square root, the standard deviation.
The story
A class has 5 students. Their scores: 60, 70, 75, 80, 95.
- Mean = (60+70+75+80+95)/5 = 380/5 = 76.
- Median = middle value when sorted = 75.
- Mode = most frequent value. Each appears once → no mode.
Now add one more student scoring 5.
- Mean = (60+70+75+80+95+5)/6 = 385/6 = 64.17. Dropped by ~12.
- Median = average of 70 and 75 = 72.5. Dropped by 2.5.
This is the single most useful intuition in statistics: outliers hurt the mean far more than the median. CSAT tests this trap regularly.
After this unit, statistics questions are 30-60 second affairs.
Why this matters for UPSC
For CSAT (Paper II, qualifying 33%):
- 3-5 questions per paper on basic statistics (mean, median, mode, range, variance, std dev).
- Plus 3-5 Data Interpretation questions that rely on these concepts.
- Real-life: All economic indicators (per capita income, CPI, IIP) are statistical aggregates.
This unit unlocks 20%+ of CSAT marks when combined with DI. Strong statistical intuition also helps in GS-III Economy.