Stop 04 · Statistics for AnalystsTopics · 3/11

Distributions (Normal, Binomial)

In short

Plot almost any measurement, like heights or exam marks, and a shape appears. Knowing the common shapes tells you which tests and summaries make sense for your data.

A normal distribution is the classic bell curve many real-world metrics approximate; a binomial distribution models the count of successes across repeated yes/no trials.

The jaadu pours marbles into a pegboard that piles them into a bell-shaped heap.

Think of it like this

Marbles through a pegboard

Drop marbles through rows of pegs. Each bounces left or right at random, yet they pile up into a smooth hill: most in the middle, few at the edges. That hill is the normal curve. Counting how many marbles went left is binomial thinking.

Watch it happen

Marks of 100 students, binned

1/5Each cell is a marks band, from lowest to highest. The number is how many students fell in it.

The big ideas

What you need to know

Normal: the bell curve

Symmetric around the mean. About 68% within 1 SD, about 95% within 2 SD.

Binomial: counting successes

n yes/no trials with the same chance p each. 'How many of 100 visitors buy?' is binomial.

Skewed data is common

Income, order value and time-on-site usually have a long right tail. They are not normal.

Always plot first

A histogram shows the shape in seconds. Don't assume normal without looking.

See it in code

Walk through the code

python

1from scipy import stats2 3# Chance a normal score is above 80 if mean=65, sd=104print(1 - stats.norm.cdf(80, loc=65, scale=10))5 6# 100 visitors, each buys with p = 0.037# Chance that 5 or more buy8print(1 - stats.binom.cdf(4, n=100, p=0.03))

1/2cdf gives the chance of being at or below 80. Subtract from 1 for above.

Two quick calculations with SciPy. The first prints about 0.067, the second about 0.18.

Save yourself the pain

Common mistakes

Oops

Assuming every metric is normally distributed.

Do this instead

Plot a histogram. Revenue and session length are usually skewed, so use medians and suitable tests.

Oops

Using the binomial when the chance changes each trial.

Do this instead

Binomial needs the same probability every trial and independent trials. Check both.

Your mission

Find the shape

~25 min

Quick check

Which of these is best modelled as binomial?

Go deeper

1Sketch a normal distribution and label the 68-95-99.7 rule.
2Identify a real metric you'd expect to be roughly normally distributed, and one that wouldn't be.
3Learn the basic shape of a binomial distribution and where it shows up (conversion rates).