Sharpen your understanding of ACT Math with this focused quiz on probability and statistics, covering essential concepts like data interpretation, measures of central tendency, independent events, and more. Ideal for students aiming to master probability skills and statistical reasoning found on the ACT Math section.
If two fair coins are flipped at the same time, what is the probability of getting exactly one head?
Explanation: There are four equally likely outcomes: HH, HT, TH, and TT. Exactly one head occurs in two outcomes: HT and TH, so the probability is 2 out of 4, which reduces to 1/2. Option 1/4 would be correct for both heads or both tails, not just exactly one head. The choices 3/4 and 2/3 are distractors that do not match the correct scenario or misinterpret how probability is calculated with independent events.
In a class, the five test scores are 70, 85, 90, 95, and 100. What is the mean (average) score for the class?
Explanation: The mean is found by summing all scores (70 + 85 + 90 + 95 + 100 = 440) and dividing by the number of students (5), which gives 88. Option 90 is the median, not the mean. Option 87 is close but is an incorrect calculation. Option 93 reflects the highest score, not the mean or any central tendency measure.
Which of the following datasets has the smallest standard deviation? (A) 2, 2, 2, 2 or (B) 4, 6, 8, 10
Explanation: Dataset A has all numbers being the same, so their standard deviation is zero, the smallest possible. Dataset B’s values are spread out, thus producing a greater standard deviation. Saying 'Both have the same standard deviation' is incorrect because their variability clearly differs. 'Cannot be determined' is inappropriate because enough information is given.
If a standard six-sided die is rolled twice, what is the probability that both rolls show a number greater than 4?
Explanation: On a six-sided die, numbers greater than 4 are 5 and 6, giving 2 options per roll. The probability for one roll is 2/6 or 1/3. For independent rolls, (1/3) × (1/3) equals 1/9. The option 1/4 miscalculates the possible favorable pairs. Option 1/6 assumes only one favorable result in two rolls, and 2/3 reflects the probability for only one roll, not both.
If a box-and-whisker plot shows a median of 60, lower quartile of 50, and upper quartile of 70, what is the interquartile range (IQR)?
Explanation: The interquartile range is calculated as the upper quartile minus the lower quartile: 70 - 50 equals 20. Option 10 confuses half of the IQR or uses the difference from median to one quartile. Option 60 could be mistaken for total spread or median value, and option 50 is simply the lower quartile, not the IQR.