Statistics basics

Story hook

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.