NBT Data Interpretation & Analysis 3 — Questions and Answers
Question 1: A box-and-whisker plot shows: minimum = 20, Q1 = 35, median = 50, Q3 = 65, maximum = 80. What is the interquartile range (IQR)?
- 20
- 25
- 30 (Correct answer)
- 45
Correct answer: 30
IQR = Q3 - Q1 = 65 - 35 = 30.
Question 2: A frequency distribution shows: scores 0–49 (15 students), 50–74 (45 students), 75–100 (40 students). What percentage of students scored below 50?
- 12%
- 15% (Correct answer)
- 18%
- 20%
Correct answer: 15%
Total: 15 + 45 + 40 = 100 students. Percentage below 50: 15 ÷ 100 = 15%.
Question 3: Two datasets have the same mean but different standard deviations (SD₁ = 2, SD₂ = 10). What can be concluded?
- Dataset 1 has a higher average
- Dataset 2 has more spread around the mean (Correct answer)
- Dataset 1 and 2 are identical
- Dataset 2 has fewer values
Correct answer: Dataset 2 has more spread around the mean
Standard deviation measures the spread of data around the mean. Dataset 2 (SD = 10) has much more variability — its values are more spread out from the mean than Dataset 1 (SD = 2).
Question 4: A regression line on a scatter plot has the equation y = 3x + 5. What does the slope (3) tell us?
- The y-intercept is 3
- For every 1-unit increase in x, y increases by 3 (Correct answer)
- The relationship is negative
- There are 3 data points
Correct answer: For every 1-unit increase in x, y increases by 3
The slope of a linear equation represents the rate of change. A slope of 3 means that for every 1-unit increase in x, the predicted value of y increases by 3.
Question 5: A researcher claims that because crime rates and ice cream sales both rise in summer, ice cream causes crime. What is wrong with this reasoning?
- Crime rates do not rise in summer
- Correlation does not imply causation — both are affected by a third variable (heat/summer) (Correct answer)
- Ice cream is not sold in summer
- The researcher has not collected enough data
Correct answer: Correlation does not imply causation — both are affected by a third variable (heat/summer)
This is a classic confounding variable (lurking variable) example. Both variables are influenced by a third factor (hot weather/summer) — not by each other. Correlation ≠ causation.
Question 6: A sample of 200 students has a mean score of 60 with a standard deviation of 10. Assuming a normal distribution, approximately what percentage of students scored between 50 and 70?
- 50%
- 58%
- 68% (Correct answer)
- 95%
Correct answer: 68%
In a normal distribution, approximately 68% of data falls within one standard deviation (±1 SD) of the mean. Mean ± 1 SD = 60 ± 10 = [50, 70]. Approximately 68% scored in this range.
NBT Data Interpretation & Analysis 3
A box-and-whisker plot shows: minimum = 20, Q1 = 35, median = 50, Q3 = 65, maximum = 80.
What is the interquartile range (IQR)?