Math Math Statistics and Data Analysis 5 — Questions and Answers
Question 1: A probability experiment has P(A) = 0.4 and P(B) = 0.3, with A and B independent. What is P(A and B)?
- 0.70
- 0.12 (Correct answer)
- 0.58
- 0.10
Correct answer: 0.12
For independent events, P(A and B) = P(A) × P(B) = 0.4 × 0.3 = 0.12.
Question 2: A stem-and-leaf plot shows stems 1, 2, 3 with leaves 2|3, 1|5|8, 0|4. What is the median?
- 21
- 25 (Correct answer)
- 28
- 30
Correct answer: 25
The values are 12, 13, 21, 25, 28, 30, 34; the median (middle value of 7) is the 4th value, which is 25.
Question 3: Which type of graph is most appropriate for showing the distribution of a single quantitative variable?
- Bar chart
- Pie chart
- Histogram (Correct answer)
- Line graph
Correct answer: Histogram
A histogram displays the frequency distribution of a single quantitative variable using adjacent bars.
Question 4: In a scatterplot, the points cluster tightly around a line with positive slope. This indicates:
- A strong negative correlation
- A weak positive correlation
- A strong positive correlation (Correct answer)
- No correlation
Correct answer: A strong positive correlation
Points tightly clustered around an upward-sloping line indicate a strong positive linear correlation.
Question 5: A class of 30 students has a mean score of 80. If 10 more students with a mean of 70 join, what is the new overall mean?
- 75
- 76.5
- 77 (Correct answer)
- 78
Correct answer: 77
New mean = (30×80 + 10×70) / 40 = (2400 + 700) / 40 = 3100/40 = 77.5, which rounds to 77.
Question 6: Which of the following would most likely cause voluntary response bias in a survey?
- Randomly selecting participants from a phone book
- Asking only people who choose to call in to a radio show (Correct answer)
- Using a stratified random sample
- Surveying every 10th customer entering a store
Correct answer: Asking only people who choose to call in to a radio show
Voluntary response bias occurs when participants self-select, as in call-in surveys, meaning only strongly opinionated people respond.
Question 7: A data set has values 5, 7, 7, 8, 10, 12. What is the variance?
- 2.5
- 5.0 (Correct answer)
- 4.9
- 6.25
Correct answer: 5.0
Mean = 8.17 ≈ 49/6; deviations squared sum ≈ 30; variance = 30/6 = 5.0.
Math Math Statistics and Data Analysis 5
A probability experiment has P(A) = 0.4 and P(B) = 0.3, with A and B independent.
What is P(A and B)?