Title: InkMaths / Statistics essentials
On every note of this deck, unless a note says otherwise:
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Front: SPOT THE ERROR
Say what is wrong with this claim:
In a histogram, the tallest bar holds the most values.
Back: Height is frequency density, so a tall narrow bar can hold fewer values than a low wide one. Area, height times width, is what counts values.

Front: CHECK YOURSELF
A firm has 900 full-time and 300 part-time staff. How many of each go into a stratified sample of 60?
Back: Full-time: 60 × 900/1200 = 45; part-time: 60 × 300/1200 = 15.

Front: STANDARD RESULT — LEARN IT
Addition rule:
P(A ∪ B) = ?
Back: P(A ∪ B) = P(A) + P(B) − P(A ∩ B)

Front: STANDARD RESULT — LEARN IT
Outlier fences:
outliers lie beyond ?
Back: Q_1 - 1.5 × IQR and Q_3 + 1.5 × IQR

Front: DEFINE
Define: actual significance level.
Back: The probability, calculated assuming the null hypothesis is true, of landing in the critical region: the test's real false-alarm rate.

Front: STANDARD RESULT — LEARN IT
Conditional probability:
P(A|B) = ?
Back: P(A|B) = P(A ∩ B)P(B)

Front: SPOT THE ERROR
Say what is wrong with this claim:
A strong correlation shows that one variable causes the other.
Back: Correlation measures how two variables move together, nothing more. A third factor can drive both, the way summer heat lifts ice cream sales and drownings at once. Causation needs an experiment, not an r value.

Front: STANDARD RESULT — LEARN IT
Variance from sums:
σ^2 = ? from Σ x and Σ x^2
Back: σ^2 = Σ x^2n - (Σ xn)^2

Front: DEFINE
Define: independent events.
Back: Events A and B are independent when P(A ∩ B) = P(A) × P(B); equivalently, when P(A|B) = P(A), so B carries no news about A.

Front: STANDARD RESULT — LEARN IT
Histograms:
frequency density = ?
Back: frequency density = frequencyclass width

Front: CHECK YOURSELF
X ~ B(20, 0.15). Write P(X ≥ 5) in calculator-ready cumulative form.
Back: P(X ≥ 5) = 1 − P(X ≤ 4): at least five means not four-or-fewer.

Front: STANDARD RESULT — LEARN IT
The sample mean's distribution:
mean of n obs of N(μ, σ^2): ?
Back: N(μ, σ^2/n)