Data Analysis Flashcards

A sample of 10 test scores has a mean of 75 and a standard deviation of 8. A student scores 91. Approximately how many standard deviations above the mean is this score?

Answer: 2

(91 − 75) / 8 = 16 / 8 = 2 standard deviations above the mean.

Among 200 cat owners surveyed, 120 also own dogs. What is the probability that a randomly selected cat owner from this group also owns a dog?

Answer: 0.6

120 / 200 = 0.60, so there is a 60% probability that a cat owner also owns a dog.

A scatterplot shows an exponential pattern, but a student fits a linear model. What is the likely consequence?

Answer: Predictions will be systematically biased for large x values

Fitting a linear model to exponential data produces systematic bias and non-random residual patterns.

In a normally distributed dataset, approximately what percentage of values fall within one standard deviation of the mean?

Answer: 68%

The empirical rule states that approximately 68% of values in a normal distribution fall within one standard deviation of the mean.

A two-way table shows 40 men and 60 women surveyed. Of the men, 25 exercise daily; of the women, 30 exercise daily. Which group has a higher relative frequency of daily exercisers?

Answer: Men, because 25/40 > 30/60

Men: 25/40 = 62.5%; Women: 30/60 = 50%, so men have a higher relative frequency.

A researcher randomly assigns participants to receive a vitamin supplement or a placebo. After 3 months, the supplement group shows significantly better energy levels. What type of study is this?

Answer: Randomized controlled experiment

Random assignment to treatment and control groups defines a randomized controlled experiment.

A set of 6 data values has a mean of 12. One value of 6 is removed. What is the new mean of the remaining 5 values?

Answer: 13.2

Original sum = 12 × 6 = 72; removing 6 leaves 66; new mean = 66 / 5 = 13.2.