STAT Data Interpretation from Graphs 4 — Questions and Answers
Question 1: A box-and-whisker plot for a dataset shows: minimum=10, Q1=25, median=40, Q3=55, maximum=80. What is the interquartile range (IQR)?
- 70
- 30 (Correct answer)
- 40
- 15
Correct answer: 30
IQR = Q3 − Q1 = 55 − 25 = 30.
Question 2: A line graph compares the growth of two populations over 10 years. Population A grows from 1,000 to 2,000; Population B grows from 500 to 1,200. Which population grew more in absolute terms?
- Population A (Correct answer)
- Population B
- They grew by the same absolute amount
- Cannot be determined
Correct answer: Population A
Population A added 1,000 people while Population B added 700 people, so A had greater absolute growth.
Question 3: A bar graph shows the number of medals won by five countries in an Olympic event. If the graph's y-axis starts at 5 instead of 0, what potential misinterpretation could occur?
- Differences between countries appear smaller than they are
- Differences between countries appear larger than they are (Correct answer)
- The total number of medals appears doubled
- No misinterpretation is possible
Correct answer: Differences between countries appear larger than they are
A truncated y-axis starting above zero makes bars appear disproportionately different, exaggerating the visual gap between countries.
Question 4: A histogram shows the distribution of ages in a sample, with most data concentrated between 20–40 and a long tail extending to age 80. What type of distribution is this?
- Symmetric (normal) distribution
- Right-skewed (positively skewed) distribution (Correct answer)
- Left-skewed (negatively skewed) distribution
- Bimodal distribution
Correct answer: Right-skewed (positively skewed) distribution
A long tail extending toward higher values (right side) defines a right-skewed or positively skewed distribution.
Question 5: A dual-axis graph shows monthly sales volume (bars, left axis) and average sale price (line, right axis). In March, volume is highest but price is lowest. What can be inferred?
- Revenue was necessarily highest in March
- High volume and low price may offset each other's revenue effects (Correct answer)
- Price drives volume in all months
- The graph contains an error
Correct answer: High volume and low price may offset each other's revenue effects
Revenue = price × volume; with the highest volume offset by the lowest price, the net effect on revenue is ambiguous without exact numbers.
Question 6: A stem-and-leaf plot displays data with stems 1–5. The stem '3' has leaves: 2, 4, 4, 7, 9. How many data values fall between 30 and 39 inclusive?
- 3
- 4
- 5 (Correct answer)
- 6
Correct answer: 5
Each leaf on stem '3' represents one value (32, 34, 34, 37, 39), giving 5 values in the 30–39 range.
Question 7: A line graph shows a city's temperature measured at 6am, 12pm, 6pm, and 12am over one day: 15°C, 28°C, 24°C, 17°C. What was the temperature range for that day?
- 9°C
- 11°C
- 13°C (Correct answer)
- 15°C
Correct answer: 13°C
Range = maximum − minimum = 28°C − 15°C = 13°C.
STAT Data Interpretation from Graphs 4
A box-and-whisker plot for a dataset shows: minimum=10, Q1=25, median=40, Q3=55, maximum=80.
What is the interquartile range (IQR)?