Cheatsheet: The shape of data: distributions and histograms

The one idea

A histogram shows the shape of data, which a center and spread cannot. Before trusting a column of data, look at its shape: skew, outliers, hidden populations, and class imbalance all show up in the picture and hide in the numbers.

What a histogram is

Step 1: chop the value range into equal bins.
Step 2: draw a bar for the count of values in each bin.
Bin width too wide  -> hides structure (a few fat bars).
Bin width too narrow -> spiky noise (one value per bin).

The shapes and what mean vs median does

Shape	Looks like	Mean vs median	Often means
Symmetric	Mirror-image halves	About equal	Balanced data
Right-skewed	Long tail to the right	Mean above median	Incomes, prices, durations, counts
Left-skewed	Long tail to the left	Mean below median	Easy-exam scores, ceilings
Uniform	All bins about equal	About equal	Fair die, no favored range
Bimodal	Two peaks	Mean in the valley (misleading)	Two populations mixed
Bell-shaped	Single peak, smooth tails	About equal	The normal distribution (own lesson)

Skew is named for where the tail points, not where the bulk sits. The mean chases the tail.

What each shape warns you about (machine learning)

You see	Likely meaning	Action
Strong skew	Bulk crammed against one edge	Consider a transform (e.g. logarithm)
Lone far-out bar / impossible spike	Outlier or data error	Investigate and clean
Two peaks	Two subpopulations in one column	Separate them or add the grouping feature
One label towering	Class imbalance (base-rate trap)	Use imbalance-aware metrics; maybe rebalance

Pitfalls to dodge

• Trusting summary numbers without seeing the shape.
• Letting bin width fool you (too wide hides, too narrow invents).
• Ignoring a second peak (two populations described by neither mean).
• Reading skew backward (it is named for the tail, not the bulk).
• Forgetting the labels have a distribution too (imbalance lives there).

Words to use precisely

• Histogram: bars showing the count of values in each bin of the range.
• Bin: one equal interval of the value range.
• Skew: a stretched tail on one side; right-skew pulls the mean up, left-skew pulls it down.
• Bimodal: two peaks; usually two mixed populations.
• Class imbalance: one target class far more common than others; a histogram of labels reveals it.