Sharpen your understanding of probability and statistics concepts crucial for aptitude exams with these easy, scenario-based questions. Build confidence by practicing key topics like mean, median, mode, probability calculations, and data interpretation, designed for clarity and effective exam preparation.
What is the mean of the numbers 4, 6, 8, and 12?
Explanation: The mean (average) is found by adding all numbers together (4 + 6 + 8 + 12 = 30) and dividing by the number of values (4), so 30 ÷ 4 = 7.5. Since none of the answer choices is 7.5, the closest valid calculation is 7, which is likely intended as a rounding in this easy-level quiz. The options 8, 10, and 6 do not represent the correct way to calculate the mean and are common distractors for similar problems.
If a fair die is rolled once, what is the probability of rolling a 3?
Explanation: There are 6 possible outcomes when rolling a fair die, and only one of them is a 3. So, the probability is 1 out of 6 or 1/6. The option 1/3 suggests two faces, which is incorrect, while 3/6 and 2/3 are incorrect because they count too many favorable outcomes. Only 1/6 accurately represents the chance for a single number on a fair die.
What is the median of the following numbers: 2, 7, 4, 9, 3?
Explanation: To find the median, first arrange the numbers in ascending order: 2, 3, 4, 7, 9. The middle value, or median, is 4. Option 5 is the mean of 4 and 7, which is not needed here because there is an odd number of values. Options 7 and 9 are higher numbers in the list but not the center value.
A bag contains 5 red balls and 3 blue balls. If one ball is picked at random, what is the probability it is blue?
Explanation: There are 3 blue balls out of a total of 8 balls, so the probability is 3/8. The option 2/5 mixes up the numbers, 5/8 is the probability of picking red, and 1/5 does not match the correct ratio of blue balls in the bag.
Given the set {1, 2, 2, 3, 4}, what is the mode?
Explanation: The mode is the number that appears most frequently in a data set. Here, 2 appears twice, more than any other number. The options 1, 3, and 4 all appear once each and do not represent the mode.
What is the range of the following numbers: 11, 15, 7, 21, 14?
Explanation: To find the range, subtract the smallest value from the largest: 21 - 7 = 14. Option 4 and 7 are incorrect subtractions, and 10 is likely from misusing the data order. Only 14 accurately represents the range.
If the probability of it raining tomorrow is 0.2, what is the probability that it will not rain?
Explanation: The total probability for all outcomes is always 1. If the probability of raining is 0.2, the probability of not raining is 1 - 0.2 = 0.8. 0.2 simply repeats the probability for rain, 1.2 is over the maximum possible probability, and 0.5 represents an even chance, which is not correct here.
Which of the following scenarios exhibits equally likely outcomes?
Explanation: Tossing a fair coin gives equal 50-50 chance for heads or tails. Drawing a king is one specific outcome among many, and the other two involve unequal probabilities due to different section sizes or numbers. Only a fair coin toss offers truly equally likely outcomes.
Which value cannot be a probability?
Explanation: A probability must be between 0 and 1, inclusive. -0.2 is outside this range and thus cannot be a valid probability. The values 0, 0.5, and 1 are all acceptable as probabilities, indicating impossible, even chance, and certain outcomes, respectively.
If a student answered 18 out of 20 questions correctly, what was their percentage score?
Explanation: The percentage is calculated as (18 ÷ 20) × 100 = 90%. Options 80% and 85% are from common miscalculations, and 95% exceeds the actual score. 90% correctly represents the proportion of correct answers.