Mathematics · Grades 11–12
Statistics & probability · Formula sheet
Rules, conditions and small examples in one printable reference.
Remember this
Combinations
Use combinations when order does not matter and items are chosen without replacement.
C(n,r) = n!/[r!(n − r)!]
10!/(3! × 7!) = 120
Permutations
Use permutations when order matters and no item is repeated.
P(n,r) = n!/(n − r)!
9!/4! = 15120
Weighted mean
Multiply each value by its frequency; divide by total frequency, not by the number of values.
weighted mean = Σ(wᵢxᵢ)/Σwᵢ
(11 × 10 + 20 × 9)/(10 + 9) = 290/19
Conditional probability from counts
Restrict the denominator to the group named in the condition.
P(A | B) = count(A and B) / count(B)
6/(6 + 19) = 6/25
Population variance
This is population variance: divide by N, not N − 1.
σ² = Σ(x − μ)²/N
μ = 19; (324 + 81 + 0 + 81 + 324)/5 = 162
Interquartile range
Use medians of the lower and upper halves for this exercise.
IQR = Q₃ − Q₁
Q₁ = 50.5; Q₃ = 94.5; IQR = 44
Further reading and review references
These are reference links, not copied exercises, institutional endorsement or proof of independent review.
Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.