Math Statistics and Data Analysis Flashcards

A probability experiment has P(A) = 0.4 and P(B) = 0.3, with A and B independent. What is P(A and B)?

Answer: 0.12

For independent events, P(A and B) = P(A) × P(B) = 0.4 × 0.3 = 0.12.

A stem-and-leaf plot shows stems 1, 2, 3 with leaves 2|3, 1|5|8, 0|4. What is the median?

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.

Which type of graph is most appropriate for showing the distribution of a single quantitative variable?

Answer: Histogram

A histogram displays the frequency distribution of a single quantitative variable using adjacent bars.

In a scatterplot, the points cluster tightly around a line with positive slope. This indicates:

Answer: A strong positive correlation

Points tightly clustered around an upward-sloping line indicate a strong positive linear correlation.

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?

Answer: 77

New mean = (30×80 + 10×70) / 40 = (2400 + 700) / 40 = 3100/40 = 77.5, which rounds to 77.

Which of the following would most likely cause voluntary response bias in a survey?

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.

A data set has values 5, 7, 7, 8, 10, 12. What is the variance?

Answer: 5.0

Mean = 8.17 ≈ 49/6; deviations squared sum ≈ 30; variance = 30/6 = 5.0.