Data Analysis & Statistical Interpretation Flashcards

A random variable X has E(X) = 5 and Var(X) = 4. What are E(2X + 3) and Var(2X + 3)?

Answer: E = 13, Var = 16

E(2X+3) = 2(5)+3 = 13; Var(2X+3) = 2²×Var(X) = 4×4 = 16.

A two-way table shows: P(A) = 0.6, P(B|A) = 0.5, P(B|A') = 0.2. What is P(B)?

Answer: 0.38

P(B) = P(B|A)P(A) + P(B|A')P(A') = 0.5(0.6)+0.2(0.4) = 0.30+0.08 = 0.38.

Data values are 5, 10, 15, 20, 25. Which transformation would most linearise the relationship if the original data appears exponential?

Answer: Taking the logarithm of each value

Taking logarithms converts an exponential relationship y = ab^x into a linear one: log y = log a + x log b.

A bag contains 4 red and 6 blue balls. Two balls are drawn without replacement. What is the probability that both are red?

Answer: 2/15

P(both red) = (4/10) × (3/9) = 12/90 = 2/15.

A data analyst calculates Spearman's rank correlation coefficient for two variables and obtains rs = −0.85. What does this indicate?

Answer: A strong negative monotonic relationship

Spearman's rs near −1 indicates a strong negative monotonic relationship (not necessarily linear).

A time series shows an upward trend with seasonal variation. Which method is most appropriate to isolate the trend?

Answer: Computing a moving average

A moving average smooths out seasonal fluctuations to reveal the underlying trend in a time series.

A sample of size n = 100 has a mean of 42 and standard deviation of 8. Using the Central Limit Theorem, what is the standard error of the mean?

Answer: 0.8

Standard error = σ/√n = 8/√100 = 8/10 = 0.8.