Math Says Yes

Concept

Uncertainty

The honest range left after measurement limits, model choices, and missing information. A single number can be useful as a midpoint, but decisions usually need plausible low and high values too. Good estimates state the assumptions that would move the answer.

Lessons

Layered estimate bands around a large mountain-like total.

Big Numbers Need Ranges

Large-scale claims are often estimates, so the honest answer includes assumptions and uncertainty.

Point estimates shown with horizontal uncertainty ranges.

Uncertainty Needs Ranges

A measured number is usually a best estimate with sampling wobble around it, so honest comparisons need ranges as well as point estimates.

Related Facts

4 min · medium

Several interval bars around a target line, with most bars crossing the target and one missing it.

A 95% confidence interval is not a 95% promise

A 95% confidence interval means the method works 95% of the time in repeated samples, not that this exact range now has a 95% chance of holding the truth.

A multi-level parking garage with its decks packed full of garbage bags instead of cars.

A parking garage can disappear into garbage math

A city can produce volumes of trash that sound impossible until you break the estimate into people, bags, and space.

A dense forest canopy beside a sparser starfield, the trees clearly more numerous.

Earth may have more trees than the Milky Way has stars

A 2015 Nature study estimated about 3.04 trillion trees on Earth, far above common estimates for stars in the Milky Way.

5 min · medium

A horizontal range bar with a center dot on the left, and a dashed threshold line with a marker crossing it on the right.

P-value vs confidence interval: what each one tells you

A p-value asks whether the data look surprising under a null model. A confidence interval asks which effect sizes remain plausible.