Why statistics matters
In data analytics, statistics helps you:
- Summarize data reliably (not just “eyeballing” charts)
- Quantify uncertainty (confidence intervals instead of single numbers)
- Compare groups fairly (hypothesis tests)
- Understand relationships (correlation vs causation)
Core vocabulary
- Population: the full set you care about
- Sample: observed subset of the population
- Parameter: a population quantity (true mean, true proportion)
- Statistic: a sample-based estimate (sample mean, sample proportion)
- Bias: systematic error (wrong sampling, leakage)
- Variance: how much an estimator varies across samples
A simple mental model
You rarely see the population. You take a sample and estimate.
- Your estimate is not exact.
- Your estimate changes if you resample.
That’s why we use:
- Distributions
- Standard error
- Confidence intervals
Common mistakes to avoid
- Correlation ≠ causation
- P-hacking (trying many tests until something is “significant”)
- Ignoring base rates (rare events)
- Selection bias (your sample isn’t representative)
- Over-trusting averages without checking spread/outliers
Minimal Python setup
import numpy as np
import pandas as pd
import scipy.stats as statsIf SciPy isn’t available in your environment, you can still follow most concepts using NumPy.
How the pieces fit together
Every statistics workflow in this phase follows roughly the same shape: you start with raw data, describe it, then use that description to reason about a population you can't fully observe.
flowchart LR A["Population
(unknown, huge)"] --> B["Sample
(what you collect)"] B --> C["Descriptive stats
(mean, median, spread)"] C --> D["Inference
(CI, hypothesis tests)"] D --> E["Decision
(ship it? investigate more?)"]
Check your understanding
What is the difference between a parameter and a statistic?
The true mean is a parameter and the sample mean is a statistic that estimates it.
Show answer
A — A parameter is a population quantity, a statistic is a sample-based estimate — The true mean is a parameter and the sample mean is a statistic that estimates it.
What is p-hacking?
It is listed among common mistakes and inflates false positives.
Show answer
A — Trying many tests until something is significant — It is listed among common mistakes and inflates false positives.
Why do analysts use standard error and confidence intervals?
You rarely see the population, so your estimate is not exact and varies across samples.
Show answer
A — The sample estimate changes if you resample — You rarely see the population, so your estimate is not exact and varies across samples.
Which is an example of selection bias?
If the sample is not representative, even a perfect test gives misleading conclusions.
Show answer
C — A sample that is not representative of the population — If the sample is not representative, even a perfect test gives misleading conclusions.
🧪 Try It Yourself
Exercise 1 – Population vs. sample mean
Tab indents. Press Escape, then Tab, to leave the editor. Control plus Enter runs the code; Control plus Shift plus Enter submits it.
Press Run to see what your code prints.Exercise 2 – Statistic vs. parameter
Tab indents. Press Escape, then Tab, to leave the editor. Control plus Enter runs the code; Control plus Shift plus Enter submits it.
Press Run to see what your code prints.Exercise 3 – Spotting selection bias
Tab indents. Press Escape, then Tab, to leave the editor. Control plus Enter runs the code; Control plus Shift plus Enter submits it.
Press Run to see what your code prints.Next
Continue to Descriptive Statistics to learn how mean, median, and variance summarize a sample before you do any inference.