IMO Practice Test — Statistics
6 Questions • 15 min • Olympiad level
15:00
Question 1 of 6
hard
The mean of 10 numbers is 20. If each number is increased by 5, the new mean is:
20
25
30
100
Explanation: Adding constant to all values increases mean by same constant
Question 2 of 6
hard
The median of the data: x, x+2, x+4, x+6, x+8 is 20. Find x.
16
18
20
22
Explanation: Median = 3rd value = x+4 = 20 → x=16? Wait, x+4=20 → x=16. But option A=16 ✓
Question 3 of 6
hard
The mode of the data 3, 5, 3, 7, 5, 9, 5, 7, 3 is:
3
5
Both 3 and 5
7
Explanation: 3 appears 3 times, 5 appears 3 times → bimodal
Question 4 of 6
hard
A histogram has class intervals 0-10, 10-20, 20-30 with frequencies 5, 12, 8. If the class width is doubled, what happens to the heights of bars?
Double
Halve
Same
Quadruple
Explanation: Frequency density = frequency/width; if width doubles, height halves
Question 5 of 6
hard
The mean of 5 observations is 15. If one observation is excluded, the mean becomes 12. The excluded observation is:
27
30
33
36
Explanation: Sum5=75, sum4=48, excluded=27
Question 6 of 6
hard
For the data 10, 12, 14, 16, 18, if 10 is replaced by 100, which measure changes the most?
Mean
Median
Mode
Range
Explanation: Mean changes from 14 to 32 (+18); median from 14 to 16 (+2); range from 8 to 90 (+82) actually range changes most! Range goes from 8 to 90. So D is correct