STAT Data Interpretation from Graphs 3 — Questions and Answers
Question 1: A time-series graph shows a company's quarterly profits over 3 years. The trend line slopes upward but individual quarters alternate high and low. What best describes this pattern?
- Consistent growth with no variation
- An overall upward trend with seasonal fluctuation (Correct answer)
- A downward trend with noise
- A cyclical pattern with no overall trend
Correct answer: An overall upward trend with seasonal fluctuation
An upward-sloping trend line combined with alternating quarterly values indicates overall growth with seasonal fluctuation.
Question 2: A bar chart shows the number of books read per month by five students: Ana=8, Ben=5, Cara=12, Dan=3, Eve=7. What is the mean number of books read?
- 6
- 7 (Correct answer)
- 8
- 5
Correct answer: 7
(8+5+12+3+7) / 5 = 35/5 = 7.
Question 3: A line graph shows two companies' stock prices. Company X starts at $50 and ends at $80; Company Y starts at $20 and ends at $38. Which company had a higher percentage growth?
- Company X
- Company Y (Correct answer)
- Both grew by the same percentage
- Cannot be determined from this information
Correct answer: Company Y
Company X grew 60% ($30/$50), while Company Y grew 90% ($18/$20), so Company Y had higher percentage growth.
Question 4: A frequency polygon has peaks at values 30, 50, and 70, with the highest peak at 50. What does this shape suggest about the distribution?
- The data is uniformly distributed
- The data is roughly symmetrical with a central peak (Correct answer)
- The data is strongly right-skewed
- The data has no central tendency
Correct answer: The data is roughly symmetrical with a central peak
A central dominant peak at 50 with roughly symmetric side peaks at 30 and 70 suggests an approximately symmetrical, bell-shaped distribution.
Question 5: A grouped bar chart compares commute times (under 30 min, 30–60 min, over 60 min) for City A and City B. City A's tallest bar is 'under 30 min' while City B's tallest bar is '30–60 min.' What can be concluded?
- City A residents always commute faster than City B residents
- City A residents more commonly have short commutes than City B residents (Correct answer)
- City B has worse public transportation than City A
- City A and City B have identical commute patterns
Correct answer: City A residents more commonly have short commutes than City B residents
The tallest bar indicates the most frequent category; City A's modal commute is under 30 minutes while City B's is 30–60 minutes.
Question 6: A scatter plot displays height (cm) on the x-axis and shoe size on the y-axis for 50 people. The correlation coefficient is 0.85. What does this value indicate?
- A weak positive correlation
- A strong positive correlation (Correct answer)
- A perfect positive correlation
- A strong negative correlation
Correct answer: A strong positive correlation
A correlation coefficient of 0.85 is close to 1, indicating a strong positive relationship between height and shoe size.
Question 7: A pie chart shows market share: Brand A = 35%, Brand B = 30%, Brand C = 20%, Brand D = 15%. If Brand A's share grows to 45% while all others shrink proportionally, what is Brand B's new approximate share?
- 25%
- 23% (Correct answer)
- 27%
- 20%
Correct answer: 23%
The remaining 55% is distributed among B, C, D originally holding 65%; Brand B's proportional share is (30/65)×55 ≈ 25.4%, closest to 25%.
STAT Data Interpretation from Graphs 3
A time-series graph shows a company's quarterly profits over 3 years.
The trend line slopes upward but individual quarters alternate high and low.
What best describes this pattern?