AQL Statistical Reasoning and Probability 1 — Questions and Answers
Question 1: What does the 'mean' of a data set represent?
- The arithmetic average, calculated by dividing the sum of all values by the number of values (Correct answer)
- The middle value when data is arranged in order
- The value that appears most frequently in the data
- The difference between the largest and smallest values
Correct answer: The arithmetic average, calculated by dividing the sum of all values by the number of values
The mean is calculated by adding all values together and dividing by the total count of values, representing the data's arithmetic center.
Question 2: What is the 'median' of the data set: 3, 7, 8, 12, 15?
- 8 (Correct answer)
- 7
- 9
- 3
Correct answer: 8
When the five values are arranged in order (3, 7, 8, 12, 15), the middle (third) value is 8, which is the median.
Question 3: A data set has values: 4, 4, 5, 7, 9, 9, 9. What is the mode?
- 9 (Correct answer)
- 4
- 6.71
- 7
Correct answer: 9
The mode is the value that appears most frequently in the data; 9 appears three times, more than any other value.
Question 4: What does a 'large standard deviation' indicate about a data set?
- The data points are spread widely from the mean (Correct answer)
- The data points are clustered closely around the mean
- The data set has many outliers below the mean
- The mean and median are very different
Correct answer: The data points are spread widely from the mean
A large standard deviation means there is high variability in the data—the values are spread far from the average.
Question 5: If you roll a fair six-sided die, what is the probability of rolling a number greater than 4?
- 1/3 (Correct answer)
- 1/2
- 1/6
- 2/3
Correct answer: 1/3
Numbers greater than 4 on a six-sided die are 5 and 6—that's 2 favorable outcomes out of 6 total, giving a probability of 2/6 = 1/3.
Question 6: What is the range of the data set: 14, 22, 7, 31, 19?
- 24 (Correct answer)
- 19
- 7
- 31
Correct answer: 24
Range = maximum − minimum = 31 − 7 = 24.
AQL Statistical Reasoning and Probability 1
What does the 'mean' of a data set represent?