TMUA Data Analysis & Statistical Interpretation 4 — Questions and Answers
Question 1: A linear regression line is given by ŷ = 3x + 7. A data point has x = 5, y = 28. What is the residual?
- 6 (Correct answer)
- −6
- 28
- 22
Correct answer: 6
Predicted ŷ = 3(5)+7 = 22; residual = observed − predicted = 28−22 = 6.
Question 2: A pie chart shows 4 sectors. Three sectors have angles 90°, 120°, and 80°. What percentage of the data does the fourth sector represent?
- 25% (Correct answer)
- 19.4%
- 20.6%
- 70°
Correct answer: 25%
Fourth angle = 360−90−120−80 = 70°; percentage = 70/360×100 ≈ 19.4%.
Question 3: A dataset contains the values 3, 7, 7, 9, 12, 15. Which statement about the mode and median is correct?
- Mode = 7, Median = 8 (Correct answer)
- Mode = 7, Median = 7
- Mode = 9, Median = 8
- Mode = 7, Median = 9
Correct answer: Mode = 7, Median = 8
The mode is 7 (appears twice); median = average of 3rd and 4th values = (7+9)/2 = 8.
Question 4: The correlation coefficient between two variables is r = 0. What does this indicate?
- There is no relationship of any kind between the variables
- There is no linear relationship between the variables (Correct answer)
- The variables are negatively correlated
- The regression line has a slope of 1
Correct answer: There is no linear relationship between the variables
r = 0 indicates no linear correlation; a non-linear relationship may still exist.
Question 5: 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?
- 67.5 kg
- 68 kg (Correct answer)
- 67 kg
- 65 kg
Correct answer: 68 kg
Combined mean = (40×65 + 60×70)/(100) = (2600+4200)/100 = 6800/100 = 68 kg.
Question 6: A normal distribution has mean μ = 50 and standard deviation σ = 5. Approximately what percentage of values lie between 40 and 60?
- 68%
- 95% (Correct answer)
- 99.7%
- 50%
Correct answer: 95%
40 and 60 are each 2 standard deviations from the mean, so approximately 95% of values lie in this range.
Question 7: 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:
- 8
- 4 (Correct answer)
- 40
- 16
Correct 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.
TMUA Data Analysis & Statistical Interpretation 4
A linear regression line is given by ŷ = 3x + 7.
A data point has x = 5, y = 28.
What is the residual?