Statistics has its own language, and the jargon can feel impenetrable. Here are the most common questions — decoded.
What's the difference between mean and median?
[Diagram: Distribution shapes] -- Symmetric: mean=median=mode (bell curve). Right-skewed: mean>median (income). Left-skewed: mean<median (easy exam). Tail direction indicates which measure is pulled.
| Feature | Mean | Median | |---------|------|--------| | Calculation | Sum ÷ count | Middle value | | Affected by outliers? | Yes (heavily) | No (resistant) | | Best for | Symmetric data | Skewed data | | Example | Average test score | Typical home price |
Rule of thumb: If the data is roughly symmetric, mean ≈ median. If mean >> median, the data is right-skewed (high outliers). If mean << median, left-skewed (low outliers).
What is standard deviation?
Standard deviation measures how far data typically falls from the mean. It's in the same units as the data.
- Low σ → data clustered near the mean
- High σ → data widely spread out
Example: Two classes both average 75% on an exam:
- Class A: σ = 5 (everyone scored 70-80)
- Class B: σ = 20 (scores ranged from 40 to 100)
Same mean, completely different story.
What is the normal distribution?
A bell-shaped curve where:
- Mean = median = mode
- 68% within 1σ of the mean
- 95% within 2σ
- 99.7% within 3σ
Many natural phenomena approximate normal distribution: heights, blood pressure, measurement errors, exam scores (in large classes).
What is the empirical rule (68-95-99.7)?
For normal distributions:
| Within | % of Data | Example (μ=100, σ=15) | |--------|-----------|----------------------| | μ ± 1σ | 68% | 85 to 115 | | μ ± 2σ | 95% | 70 to 130 | | μ ± 3σ | 99.7% | 55 to 145 |
Practical use: If your score is 130 on an IQ test (μ=100, σ=15), you're 2σ above average — in the top 2.5%.
What is variance?
Variance is standard deviation squared (σ²). It measures spread in squared units, which is less intuitive but mathematically convenient.
- Variance = average of squared deviations from the mean
- Standard deviation = √Variance
Always report standard deviation (same units as data), not variance.
Sample vs. Population — what's the difference?
| Feature | Population | Sample | |---------|-----------|--------| | What it is | Every member | A subset | | Symbol | σ (sigma) | s | | Variance divides by | n | n − 1 | | When to use | You have ALL the data | You have PART of the data |
Example: All 200 students in a school → population. 30 students surveyed → sample.
The Trench Truth: "Average" is ambiguous — it could mean mean, median, or mode. When someone says "the average is X," ask which measure they used. A company reporting "average salary ₹12L" (mean) vs "average salary ₹6L" (median) tells very different stories about pay equity.
Further Reading
Related: Standard Deviation Calculator | Derivative Calculator | Square Root Calculator | Quadratic Formula Calculator | Integral Calculator | Circle Calculator | Area Converter
Discussion
Loading comments...