STAT Analysis of Tables and Charts 4 — Questions and Answers
Question 1: A chart shows annual profits for a company: Year 1 = $200K, Year 2 = $180K, Year 3 = $220K, Year 4 = $210K, Year 5 = $250K. What is the average annual profit?
- $210K
- $212K (Correct answer)
- $200K
- $215K
Correct answer: $212K
Sum = $200K + $180K + $220K + $210K + $250K = $1,060K; average = $1,060K ÷ 5 = $212K.
Question 2: A table shows that 3 out of every 8 items produced are defective. If 640 items are produced, how many are expected to be defect-free?
- 240
- 400 (Correct answer)
- 480
- 320
Correct answer: 400
Defective = (3/8) × 640 = 240; defect-free = 640 − 240 = 400.
Question 3: A graph displays data points for years 2015-2020. The trend line (line of best fit) suggests the value will reach 100 in 2023. This prediction is an example of:
- Interpolation
- Extrapolation (Correct answer)
- Correlation
- Regression error
Correct answer: Extrapolation
Predicting a value beyond the range of existing data (past 2020) is called extrapolation, which carries greater uncertainty than interpolation.
Question 4: A table compares two products' sales over four quarters. Product A totals 1,200 units; Product B totals 900 units. In Q3, A sold 400 and B sold 350. Which statement is supported by the data?
- Product B outsold Product A in Q3
- Product A had greater total annual sales than Product B
- Product B had a higher Q3 share of its annual total than Product A (Correct answer)
- Product A sold more in Q3 than in any other quarter
Correct answer: Product B had a higher Q3 share of its annual total than Product A
B's Q3 share = 350/900 ≈ 38.9%; A's Q3 share = 400/1,200 ≈ 33.3%, so B devoted a larger fraction of its annual total to Q3.
Question 5: A pie chart shows budget allocation: Personnel 50%, Equipment 20%, Research 15%, Admin 10%, Miscellaneous 5%. If the budget is cut by 20% overall but personnel costs remain fixed, which statement must be true?
- Research spending doubles as a percentage
- Personnel now represents more than 50% of the new budget (Correct answer)
- Equipment costs increase in absolute terms
- Admin spending is now 12% of the total
Correct answer: Personnel now represents more than 50% of the new budget
If the total budget shrinks but the fixed personnel cost stays the same, personnel's share of the reduced budget rises above 50%.
Question 6: A line graph shows temperature readings (°C) taken every 2 hours: 6am=14°, 8am=17°, 10am=22°, 12pm=26°, 2pm=28°, 4pm=25°, 6pm=20°. Between which two consecutive readings was the rate of temperature increase greatest?
- 6am–8am
- 8am–10am (Correct answer)
- 10am–12pm
- 12pm–2pm
Correct answer: 8am–10am
The rises are: 3°, 5°, 4°, 2° for the first four intervals; the jump of 5° between 8am and 10am is the largest.
Question 7: A table shows that Country X spends 6% of GDP on education and Country Y spends 8% of GDP. Country X has a GDP of $500 billion and Country Y has a GDP of $300 billion. Which country spends more on education in absolute terms?
- Country Y, because it has a higher percentage
- Country X, because 6% of $500B exceeds 8% of $300B (Correct answer)
- They spend equal amounts
- Cannot be determined from the data
Correct answer: Country X, because 6% of $500B exceeds 8% of $300B
Country X: 6% × $500B = $30B; Country Y: 8% × $300B = $24B; Country X spends more in absolute terms.
STAT Analysis of Tables and Charts 4
A chart shows annual profits for a company: Year 1 = $200K, Year 2 = $180K, Year 3 = $220K, Year 4 = $210K, Year 5 = $250K.
What is the average annual profit?