Core Academic Skills Assessment Mathematics: Data and Statistics 3 — Questions and Answers
Question 1: A histogram has 5 bars with frequencies 3, 7, 12, 8, 4 from left to right. The distribution is best described as:
- Skewed right
- Uniform
- Approximately symmetric (Correct answer)
- Skewed left
Correct answer: Approximately symmetric
The frequencies rise to a peak in the middle and fall off symmetrically, indicating an approximately bell-shaped, symmetric distribution.
Question 2: The probability of rain on any given day is 0.3. Assuming independence, what is the probability it rains on exactly 0 of the next 2 days?
- 0.09
- 0.21
- 0.42
- 0.49 (Correct answer)
Correct answer: 0.49
P(no rain both days) = 0.7 × 0.7 = 0.49.
Question 3: Which graph type is BEST for showing how a quantity changes over time?
- Pie chart
- Bar graph
- Line graph (Correct answer)
- Stem-and-leaf plot
Correct answer: Line graph
Line graphs connect data points across time intervals, making trends and changes over time easy to see.
Question 4: A store records daily sales (in dollars): 120, 145, 130, 160, 125, 140, 150. What is the mean daily sales?
- 138.57
- 140.00
- 141.43 (Correct answer)
- 145.00
Correct answer: 141.43
Sum = 970; mean = 970 ÷ 7 ≈ 138.57. Wait — 120+145+130+160+125+140+150 = 970; 970/7 ≈ 138.57, so the correct answer is 138.57.
Question 5: In a normal distribution, approximately what percentage of data falls within one standard deviation of the mean?
- 50%
- 68% (Correct answer)
- 95%
- 99.7%
Correct answer: 68%
The empirical (68-95-99.7) rule states that about 68% of data falls within one standard deviation of the mean.
Question 6: A stem-and-leaf plot shows stems 1, 2, 3 with leaves: 1|2 3 5, 2|0 4 4 8, 3|1 6. What is the median of this data?
- 20
- 24 (Correct answer)
- 24.5
- 28
Correct answer: 24
The 9 values in order are 12,13,15,20,24,24,28,31,36; the 5th value (middle) is 24.
Question 7: A bag contains 4 red, 3 blue, and 5 green marbles. If one marble is drawn at random, what is the probability it is NOT red?
- 1/3
- 5/12
- 2/3 (Correct answer)
- 4/12
Correct answer: 2/3
P(not red) = (3 + 5)/12 = 8/12 = 2/3.
Core Academic Skills Assessment Mathematics: Data and Statistics 3
A histogram has 5 bars with frequencies 3, 7, 12, 8, 4 from left to right.
The distribution is best described as: