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Descriptive & Inferential Statistics

In short

You'll almost never have data on everyone. Statistics helps you describe the data you do have, then make careful claims about the people you didn't measure.

Descriptive statistics summarize a dataset (mean, variance, distribution shape); inferential statistics let you draw conclusions about a wider population from a sample — both used constantly in EDA and evaluation.

The mascot lifts one mango out of a big wooden crate at a fruit stall.

Think of it like this

Buying a crate of mangoes

At the fruit market you can't taste all 100 mangoes. You pick five, note how sweet and ripe they are, and decide about the whole crate. Describing your five is descriptive stats. Guessing about the crate is inferential stats.

Watch it happen

From five mangoes to the whole crate

Population

Sample

Describe

Infer

Decide

1/5The population is everything you care about: all users, or the whole crate.

The big ideas

What you need to know

Centre: mean and median

The mean is pulled by extreme values. The median, the middle value, isn't. Report both when data is skewed.

Spread: standard deviation

How far values usually sit from the mean. Two groups can share a mean but differ wildly in spread.

Random samples matter

Inference only works if the sample fairly represents the population. Biased samples give confident wrong answers.

Intervals beat single numbers

A confidence interval shows a likely range for the true value, not just one guess.

See it in code

Walk through the code

python

1import numpy as np2from scipy import stats3 4sample = np.array([42, 55, 38, 61, 47, 52, 49, 58, 44, 50])  # minutes on app5 6print(sample.mean(), np.median(sample), sample.std(ddof=1))7 8ci = stats.t.interval(0.95, df=len(sample) - 1,9                      loc=sample.mean(), scale=stats.sem(sample))10print(ci)   # likely range for ALL users' average

1/3Ten users' daily minutes on an app: our sample.

Line 6 describes the ten users you have. Lines 8 to 10 make a careful guess about every user.

Save yourself the pain

Common mistakes

Oops

Reporting only the mean for salaries or house prices.

Do this instead

Show the median too. A few very large values drag the mean far from a typical person.

Oops

Surveying only your college friends and claiming it's true for 'Indian students'.

Do this instead

Say who the sample represents, or collect a fairer sample before generalising.

Your mission

Describe and infer

~25 min

Quick check

A sample of 10 users gives a 95% confidence interval of 46 to 53 minutes. What happens if you sample 1,000 users instead?

Go deeper

1Calculate mean, median, variance and standard deviation on a sample dataset by hand.
2Learn the difference between a population parameter and a sample statistic.
3Practice explaining why sample size affects how confident you can be in a conclusion.