Statistics & Probability Formula Sheet (Grade 12 CAPS)

Mean, standard deviation, regression, correlation and probability rules for Grade 12 CAPS statistics and probability, with NSC Paper 2 exam notes.

Statistics and probability are the most calculator-driven sections of NSC Paper 2. Knowing which statistical mode to use is as important as the formulas themselves.

Formulas

Formula	Expression	Note
Mean	`x̄ = Σx / n`	For grouped data use the midpoint of each interval.
Variance	`σ² = Σ(x − x̄)² / n`	Standard deviation is the square root of the variance.
Least squares regression line	`ŷ = a + bx`	Read a and b from the calculator's regression mode.
Correlation coefficient	`r, −1 ≤ r ≤ 1`	\|r\| close to 1 means a strong linear relationship.
Addition rule	`P(A or B) = P(A) + P(B) − P(A and B)`	Mutually exclusive events have P(A and B) = 0.
Complementary events	`P(not A) = 1 − P(A)`	Fastest route for 'at least one' questions.
Independent events	`P(A and B) = P(A) × P(B)`	Use this identity to prove or disprove independence.
Fundamental counting principle	`n₁ × n₂ × … × nₖ`	Arrangements of n different items = n!

How to use them

Identify outliers using the five-number summary before commenting on skewness.
For 'at least one' probability, subtract from 1.
State whether repetition is allowed in counting questions before multiplying.
Worked example: if P(A) = 0.5, P(B) = 0.4 and P(A or B) = 0.7, then P(A and B) = 0.5 + 0.4 − 0.7 = 0.2. Since P(A) × P(B) is also 0.2, A and B are independent.

Frequently asked questions

Are all Statistics & Probability formulas given in the NSC exam?

Some are printed on the official information sheet, but not all. Treat every formula on this page as examinable and learn it with a worked example so you recognise when to use it.

Which NSC paper tests Statistics & Probability?

Statistics & Probability is examined in Paper 2 of the NSC Mathematics examination.

How do I practise these formulas?

Snap a statistics & probability question into the Snap&Learn AI solver — it shows the substitution and every method mark the way the NSC memo does.

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