IMO Practice Test — Statistics

6 Questions • 15 min • Olympiad level

15:00
Question 1 of 6 medium
The mean of the following frequency distribution is 25. Find the missing frequency f: Class 0-10(5),10-20(8),20-30(12),30-40(f),40-50(3)
10
11
12
13
Explanation: Midpoints: $5, 15, 25, 35, 45$. $\sum f = 5+8+12+f+3 = 28+f$. $\sum fx = 5 \times 5 + 8 \times 15 + 12 \times 25 + 35f + 3 \times 45 = 580 + 35f$. Setting the mean to $25$: $\frac{580+35f}{28+f}=25 \Rightarrow 580+35f=700+25f \Rightarrow 10f=120 \Rightarrow f=12$.