Multi-Step Data Analysis and Graphs Flashcards

A company's annual revenue (in millions) over five years was: Year 1: $120M, Year 2: $144M, Year 3: $172.8M, Year 4: $207.4M, Year 5: $248.8M. What was the approximate average percentage growth rate per year? (A) 15% (B) 18% (C) 20% (D) 22%

Answer: 20%

Each year the revenue grows by exactly 20%: 120 × 1.2 = 144, 144 × 1.2 = 172.8, etc. The answer is 20%.

A bar chart shows quarterly sales for two products: Product A: Q1=40, Q2=55, Q3=70, Q4=85 (units) Product B: Q1=80, Q2=70, Q3=60, Q4=50 (units) In which quarter does the combined total first exceed 120 units? (A) Q1 (B) Q2 (C) Q3 (D) Q4

Answer: Q2

Q1: 40+80=120 (not exceeding). Q2: 55+70=125 > 120. The combined total first exceeds 120 in Q2.

A pie chart shows the distribution of 360 survey respondents by preferred news source: TV = 30%, Online = 45%, Print = 15%, Radio = 10%. How many more respondents prefer Online compared to the combined total of Print and Radio? (A) 54 (B) 72 (C) 81 (D) 90

Answer: 72

Online: 45% × 360 = 162. Print + Radio: (15% + 10%) × 360 = 25% × 360 = 90. Difference: 162 − 90 = 72.

A line graph shows a city's population (in thousands) from 2000 to 2020 in 5-year intervals: 2000=200, 2005=230, 2010=272, 2015=306, 2020=340. Between which two 5-year periods was the absolute increase in population the greatest? (A) 2000–2005 (B) 2005–2010 (C) 2010–2015 (D) 2015–2020

Answer: 2005–2010

Increases: 2000–05: 30K; 2005–10: 42K; 2010–15: 34K; 2015–20: 34K. The 2005–2010 period had the largest absolute increase of 42,000.

A table shows test scores for two classes: Class A: Mean = 78, Standard Deviation = 5, n = 30 Class B: Mean = 82, Standard Deviation = 12, n = 20 Which class had greater score variability, and by approximately what factor? (A) Class A; variability 2.4 times greater (B) Class B; variability 2.4 times greater (C) Class A; variability 1.5 times greater (D) Class B; variability 1.5 times greater

Answer: Class B; variability 2.4 times greater

Standard deviation measures variability. Class B: SD=12; Class A: SD=5. 12/5 = 2.4. Class B had 2.4× greater variability.

A scatterplot shows the relationship between hours studied per week (x-axis, range 0–20) and exam score (y-axis, range 40–100). The best-fit line has the equation y = 3x + 50. A student studies 15 hours per week. What score does the model predict, and how does it compare to a student who studies 10 hours? (A) Predicts 95; 15 points higher than the 10-hour student (B) Predicts 95; 10 points higher than the 10-hour student (C) Predicts 100; 20 points higher than the 10-hour student (D) Predicts 90; 20 points higher than the 10-hour student

Answer: Predicts 95; 15 points higher than the 10-hour student

15 hours: y = 3(15) + 50 = 95. 10 hours: y = 3(10) + 50 = 80. Difference: 95 − 80 = 15 points.

A table shows monthly electricity costs for an office building: Jan–Mar (avg): $1,200/month Apr–Jun (avg): $900/month Jul–Sep (avg): $1,500/month Oct–Dec (avg): $1,050/month What is the total annual electricity cost? (A) $13,800 (B) $13,950 (C) $14,100 (D) $14,400

Answer: $13,800

Each average applies to 3 months: (1200×3) + (900×3) + (1500×3) + (1050×3) = 3600 + 2700 + 4500 + 3150 = $13,950.

A double bar chart compares men's and women's marathon finish times (in minutes) across 4 age groups: Age 20–29: Men=210, Women=235 Age 30–39: Men=215, Women=242 Age 40–49: Men=225, Women=255 Age 50–59: Men=240, Women=275 In which age group is the absolute difference between men's and women's times the greatest? (A) 20–29 (B) 30–39 (C) 40–49 (D) 50–59

Answer: 50–59

Differences: 20–29: 25min; 30–39: 27min; 40–49: 30min; 50–59: 35min. The 50–59 age group has the greatest difference.

An investment portfolio had the following returns over 4 years: Year 1: +20%, Year 2: −10%, Year 3: +25%, Year 4: −5%. What was the approximate net percentage change over all 4 years? (A) +23% (B) +28% (C) +30% (D) +35%

Answer: +28%

Net return = 1.20 × 0.90 × 1.25 × 0.95 = 1.08 × 1.25 × 0.95 = 1.35 × 0.95 = 1.2825 ≈ 28.25% gain.

A histogram shows the distribution of test scores for 100 students: 50–59: 5 students 60–69: 15 students 70–79: 35 students 80–89: 30 students 90–99: 15 students What percentage of students scored below 80? (A) 45% (B) 50% (C) 55% (D) 60%

Answer: 55%

Students below 80: 5 + 15 + 35 = 55. 55/100 = 55%.

A two-way table shows survey results on coffee preference by age group: Under 30: Coffee=40, Tea=60, Total=100 Over 30: Coffee=90, Tea=60, Total=150 Total: Coffee=130, Tea=120, Grand Total=250 What percentage of coffee drinkers are over 30? (A) 60% (B) 65% (C) 69% (D) 72%

Answer: 69%

Coffee drinkers over 30: 90. Total coffee drinkers: 130. 90/130 ≈ 0.692 = 69.2% ≈ 69%.

A stacked bar chart shows the composition of a city's workforce (1,000 workers total): Government 25%, Private sector 55%, Self-employed 15%, Other 5%. If the workforce grows by 20% next year with all proportions staying the same, how many more private sector workers will there be? (A) 100 (B) 110 (C) 120 (D) 130

Answer: 110

Current private sector: 55% × 1000 = 550. New total: 1200. New private sector: 55% × 1200 = 660. Increase: 660 − 550 = 110.

A line graph shows two companies' quarterly profits (in $M): Company X: Q1=10, Q2=14, Q3=19, Q4=25 Company Y: Q1=22, Q2=20, Q3=18, Q4=15 In which quarter do the lines intersect (i.e., Company X's profit first equals or exceeds Company Y's)? (A) Q2 (B) Q3 (C) Q4 (D) They never intersect within the given data

Answer: Q4

Q1: X=10 Y=18. Actually X first exceeds Y at Q3. But wait: we need when X first equals OR exceeds Y. At Q3, X=19 > Y=18, so Q3 is correct.

A table shows the number of defective items per 1,000 produced at three factories over two years: Factory A: Year 1=25, Year 2=18 Factory B: Year 1=40, Year 2=28 Factory C: Year 1=15, Year 2=12 Which factory achieved the greatest percentage reduction in defects? (A) Factory A (B) Factory B (C) Factory C (D) Factories A and B tied

Answer: Factory B

A: (25−18)/25 = 28% reduction. B: (40−28)/40 = 30% reduction. C: (15−12)/15 = 20% reduction. Factory B had the greatest percentage reduction at 30%.

A graph shows that a city's carbon emissions (in million tons) follow the equation E = −0.4t + 12, where t = years after 2000. According to this model, in what year will emissions reach zero? (A) 2025 (B) 2028 (C) 2030 (D) 2032

Answer: 2030

Set E = 0: 0 = −0.4t + 12 → 0.4t = 12 → t = 30. Year 2000 + 30 = 2030.

A pie chart shows that a school's budget is divided as follows: Instruction 48%, Administration 18%, Facilities 14%, Technology 12%, Other 8%. The total budget is $5 million. How much more is spent on Instruction than on Administration and Technology combined? (A) $800,000 (B) $900,000 (C) $1,000,000 (D) $1,200,000

Answer: $1,000,000

Instruction: 48% × $5M = $2.4M. Admin + Tech: (18%+12%) × $5M = 30% × $5M = $1.5M. Difference: $2.4M − $1.5M = $0.9M = $900,000.

A scatter plot shows data points that suggest a strong positive correlation between advertising spend and sales revenue. The correlation coefficient is r = 0.92. What does this tell us? (A) Advertising spending causes higher sales (B) About 85% of the variance in sales is explained by advertising spend (C) For every $1 increase in advertising, sales increase by exactly $0.92 (D) The relationship is linear and perfectly predictable

Answer: About 85% of the variance in sales is explained by advertising spend

r² = 0.92² ≈ 0.846. About 84.6% ≈ 85% of the variance in sales is explained by advertising spend. Correlation does not imply causation.

A table shows the number of applications and acceptances at a university over 3 years: Year 1: Applications=8,000, Acceptances=1,200 Year 2: Applications=9,500, Acceptances=1,330 Year 3: Applications=11,000, Acceptances=1,430 In which year was the acceptance rate highest? (A) Year 1 (B) Year 2 (C) Year 3 (D) All years had the same acceptance rate

Answer: Year 1

Year 1: 1200/8000 = 15%. Year 2: 1330/9500 ≈ 14%. Year 3: 1430/11000 = 13%. Year 1 had the highest acceptance rate.

A graph shows exponential population growth modeled by P = 500 × 2^(t/10), where t = years. What is the population at t = 30? (A) 2,000 (B) 3,000 (C) 4,000 (D) 6,000

Answer: 4,000

P = 500 × 2^(30/10) = 500 × 2^3 = 500 × 8 = 4,000.

A frequency table shows the grades of 40 students: A=8, B=14, C=12, D=4, F=2. What is the probability that a randomly selected student earned either a B or C? (A) 0.55 (B) 0.60 (C) 0.65 (D) 0.70

Answer: 0.65

B + C = 14 + 12 = 26. P = 26/40 = 0.65.