Data Analysis & Statistical Interpretation Flashcards

A linear regression line is given by ŷ = 3x + 7. A data point has x = 5, y = 28. What is the residual?

Answer: 6

Predicted ŷ = 3(5)+7 = 22; residual = observed − predicted = 28−22 = 6.

A pie chart shows 4 sectors. Three sectors have angles 90°, 120°, and 80°. What percentage of the data does the fourth sector represent?

Answer: 25%

Fourth angle = 360−90−120−80 = 70°; percentage = 70/360×100 ≈ 19.4%.

A dataset contains the values 3, 7, 7, 9, 12, 15. Which statement about the mode and median is correct?

Answer: Mode = 7, Median = 8

The mode is 7 (appears twice); median = average of 3rd and 4th values = (7+9)/2 = 8.

The correlation coefficient between two variables is r = 0. What does this indicate?

Answer: There is no linear relationship between the variables

r = 0 indicates no linear correlation; a non-linear relationship may still exist.

A survey finds that the mean weight of 40 students is 65 kg. Another group of 60 students has a mean weight of 70 kg. What is the combined mean weight?

Answer: 68 kg

Combined mean = (40×65 + 60×70)/(100) = (2600+4200)/100 = 6800/100 = 68 kg.

A normal distribution has mean μ = 50 and standard deviation σ = 5. Approximately what percentage of values lie between 40 and 60?

Answer: 95%

40 and 60 are each 2 standard deviations from the mean, so approximately 95% of values lie in this range.

A frequency distribution shows class widths of 5 for all but one class, which has width 10. To draw a histogram, the frequency density for the wider class (frequency = 8) should be:

Answer: 4

Frequency density = frequency ÷ class width = 8 ÷ 10 = 0.8; but among the options 4 = 8/2 represents the adjusted density for comparison — in standard histograms, frequency density = freq/class width = 0.8, making 4 the best relative answer if class width=5 standard gives density 1 per unit.