Answer:
33
Explanation:
μ₁ = mean age of women
w = age of women
wₙ = number of women
μ₂ = mean age of men
m = age of men
mₙ = number of men
∑w = sum of the ages of all the women
∑m = sum of the ages of all the men
∑(w + m) = sum of the ages of all men and women
μ₀ = mean age of all people in the office
(w + n)ₙ = number of men and women
Formula for mean:
μ₀ = ∑(w + m)/(w + m)ₙ
Sum of the ages of everyone divided by the number of people
∑(w + m) = ∑w + ∑m
μ₁ = 35
wₙ = 12
∑w = 35 × 12
= 420
μ₂ = 31
mₙ = 8
∑m = 31 × 8
= 248
∑(w + m) = 420 + 248
= 668
(w + m)ₙ = wₙ + mₙ
(w + m)ₙ = 12 + 8
= 20
μ₀ = ∑(w + m)/(w + m)ₙ
μ₀ = 668/20
μ₀ = 33.4 → 33 (to the nearest year)