IMO Practice Test — Statistics
6 Questions • 20 min • Olympiad level
20:00
Question 1 of 6
hard
If the mean of 9 observations is 12 and the mean of another 11 observations is 18, the mean of all observations together is:
15.3
15
16
14.5
Explanation: Combined mean = (9×12 + 11×18)/20 = 306/20 = 15.3.
Question 2 of 6
hard
The variance of data 3, 3, 7, 7 is:
4
2
8
16
Explanation: Mean = 5. Squared deviations = 4,4,4,4. Variance = 16/4 = 4.
Question 3 of 6
hard
If each observation is multiplied by −2, the new standard deviation will be:
−2 times the original
2 times the original
4 times the original
Unchanged
Explanation: Standard deviation is always positive. When data is multiplied by a constant k, the new SD is |k| × original SD. Here, |−2| = 2.
Question 4 of 6
hard
In a frequency distribution, the sum of frequencies is 50, median is 28, and the cumulative frequency of the class preceding the median class is 14. If the frequency of the median class is 10 and class width is 10, the lower boundary of the median class is:
17
20
22
25
Explanation: Using Median = L + [ (N/2 − CF) / f ] × h. 28 = L + [ (25 − 14) / 10 ] × 10. 28 = L + 11. Lower limit L = 17.
Question 5 of 6
hard
The mean and variance of 20 observations are 10 and 4 respectively. On checking, it was found that an observation 9 was incorrect and the correct value was 11. The new mean is:
10.0
10.1
10.2
10.5
Explanation: Original sum = 20 × 10 = 200. New sum = 200 − 9 + 11 = 202. New mean = 202 / 20 = 10.1.
Question 6 of 6
hard
The standard deviation of data 3, 3, 7, 7 is:
2
4
√8
1
Explanation: Variance = 4, so standard deviation = 2.