AST Data Analysis and Statistics 2 — Questions and Answers
Question 1: A data set has values: 4, 8, 6, 10, 12. What is the mean?
- 7
- 8 (Correct answer)
- 9
- 10
Correct answer: 8
(4 + 8 + 6 + 10 + 12) / 5 = 40 / 5 = 8.
The mean (arithmetic average) is the sum of all values divided by the count. Sum = 4 + 8 + 6 + 10 + 12 = 40. Count = 5. Mean = 40 / 5 = 8.
Question 2: In a normal distribution, approximately what percentage of data falls within one standard deviation of the mean?
- 50%
- 68% (Correct answer)
- 75%
- 95%
Correct answer: 68%
The empirical rule states approximately 68% of data falls within ±1 standard deviation.
The empirical rule for normal distributions: ~68% of data falls within ±1 SD of the mean, ~95% within ±2 SD, and ~99.7% within ±3 SD. This rule is fundamental to statistical analysis and hypothesis testing on the ACT.
Question 3: If a bar chart shows sales of $200, $350, $150, and $300 for four quarters, what were the total annual sales?
- $900
- $950
- $1,000 (Correct answer)
- $1,050
Correct answer: $1,000
200 + 350 + 150 + 300 = $1,000.
To find annual totals from a bar chart, sum all displayed values: $200 + $350 + $150 + $300 = $1,000. Reading data from charts accurately is a key ACT science and math skill.
Question 4: A pie chart shows 40% for category A, 35% for B, and the rest for C. What percentage is C?
- 15%
- 20%
- 25% (Correct answer)
- 30%
Correct answer: 25%
100% - 40% - 35% = 25%.
In a pie chart, all categories together represent 100%. Subtract the known categories: 100% - 40% - 35% = 25%. Category C represents 25% of the total.
Question 5: In a data set of 9 numbers sorted in ascending order, which position is the median?
- 4th
- 5th (Correct answer)
- 6th
- 7th
Correct answer: 5th
For n = 9, the median is at position (9+1)/2 = 5th.
For an odd number of values n, the median is at position (n + 1)/2. With 9 values: (9 + 1)/2 = 5. The 5th value in the sorted list is the median. For an even number of values, you average the two middle values.
Question 6: A probability experiment is run 400 times. Event A occurs 100 times. What is the experimental probability of A?
- 0.20
- 0.25 (Correct answer)
- 0.30
- 0.40
Correct answer: 0.25
P(A) = 100/400 = 0.25.
Experimental (empirical) probability is calculated from observed results: P(A) = favorable outcomes / total trials = 100/400 = 1/4 = 0.25. This differs from theoretical probability, which is based on equally likely outcomes.
AST Data Analysis and Statistics 2
A data set has values: 4, 8, 6, 10, 12.
What is the mean?