- A lab measured the masses of 40 small samples. The histogram shows the number of samples in each mass interval (in grams). According to the histogram, what fraction of the samples have mass between 20 g and 40 g inclusive of the endpoints (i.e., the 20–29 and 30–39 bins)? Express the answer as a simplified fraction.
Answer: 83
We need to find what fraction of the 40 samples have mass between 20g and 40g, which includes the 20-29 and 30-39 bins. From the histogram, the 20-29 bin contains 10 samples and the 30-39 bin contains 5 samples, totaling 15 samples. The fraction is 15/40 = 3/8 when simplified. Be careful to include both bins that fall within the specified range. - A delivery company recorded the total miles driven each day for one week. The line graph shows miles driven from Monday through Sunday. By how many miles did the total increase from Tuesday to Friday?
Answer: 60 miles
The question asks for the increase in miles driven from Tuesday to Friday. From the line graph, Tuesday's point shows 120 miles and Friday's point shows 180 miles on the y-axis. The increase is 180 - 120 = 60 miles. Students often make errors by reading the wrong days or by calculating the difference in reverse order (Tuesday minus Friday instead of Friday minus Tuesday).
- A gym tracked the number of new memberships sold from January to May. The line graph shows the monthly totals. According to the graph, what is the total number of new memberships sold in March and April combined?
Answer: 80 memberships
The question asks for the total number of new gym memberships sold in March and April combined, based on the line graph. On the graph, the point for March is at 45 memberships, and for April at 35, so add these specific monthly values. The total is 45 + 35 = 80 memberships. Avoid comparing the months or subtracting instead of adding, as the question specifies 'combined.' A key error might be misreading the scale on the y-axis, perhaps confusing it with cumulative totals rather than monthly.
- A family's monthly budget is summarized in the pie chart: Rent 40%, Food 25%, Transportation 15%, Savings 10%, and Other 10%. If the total monthly budget is $2,000, how much money is spent on Food?
Answer: $500
The question asks how much money the family spends on Food from their $2,000 monthly budget, based on the pie chart. The pie chart shows Food as 25% of the total budget, so locate that sector and confirm its percentage label. Calculate 25% of $2,000: 0.25 × 2,000 = $500. Ensure the percentages add up to 100% (40% + 25% + 15% + 10% + 10% = 100%) to verify the chart's accuracy. A common error is misreading the percentage as 20% or 30%, leading to incorrect amounts like $400 or $600, so double-check the labels.
- A science club measured the temperature (in °C) of a chemical solution at five times during an experiment. The line graph shows the temperature at 0, 2, 4, 6, and 8 minutes. What is the average rate of change in temperature from 2 minutes to 8 minutes, in °C per minute?
Answer: −1.0 °C/min
To find the average rate of change, we need the temperatures at 2 minutes and 8 minutes. From the graph, at 2 minutes the temperature is 24°C, and at 8 minutes it's 18°C. The change is 18 - 24 = -6°C over a time period of 8 - 2 = 6 minutes. Average rate = -6°C ÷ 6 min = -1.0°C/min. The negative sign indicates the temperature is decreasing. - A city's transportation department tracked the average weekday ridership (in thousands of riders) for four transit options in April. The bar graph shows the average weekday ridership for Bus, Subway, Tram, and Ferry. According to the graph, what is the total average weekday ridership (in thousands) for Bus and Tram combined?
Answer: 30 thousand
The question asks for the combined average weekday ridership for Bus and Tram. Looking at the bar graph, the Bus bar reaches up to 20 thousand riders (at the 20 mark on the y-axis), and the Tram bar reaches up to 10 thousand riders (at the 10 mark). Adding these values: 20 thousand + 10 thousand = 30 thousand riders total. A common error would be misreading the scale increments or confusing the bar heights.
- A local market recorded the price of apples (in dollars per pound) over 6 days. The line graph shows the price each day. On which day was the price closest to the average (mean) price over the 6 days?
Answer: Day 3
To find which day's price was closest to the average, we first calculate the mean price over 6 days. From the graph: Day 1: $2.00, Day 2: $2.20, Day 3: $2.40, Day 4: $2.60, Day 5: $2.80, Day 6: $3.00. Mean = (2.00 + 2.20 + 2.40 + 2.60 + 2.80 + 3.00)/6 = $2.50. Distances from mean: Day 1: 0.50, Day 2: 0.30, Day 3: 0.10, Day 4: 0.10, Day 5: 0.30, Day 6: 0.50. Day 3 is closest to the mean.
- A bar graph shows the number of laptops sold by a store in four quarters: Q1 120, Q2 150, Q3 135, Q4 165. According to the graph, what percent increase in laptops sold occurred from Q1 to Q4? (Round to the nearest whole percent.)
Answer: 38%
The question asks for the percent increase from Q1 (120 laptops) to Q4 (165 laptops). The increase is: 165 - 120 = 45 laptops. The percent increase is: (45/120) × 100% = 37.5%, which rounds to 38%. A common error would be using Q4 as the denominator instead of Q1, or forgetting to multiply by 100 to convert to a percentage.
- The bar graph shows the number of pages read by four students (Alex, Bri, Chen, and Dev) over the weekend. A separate note says each student planned to read 60 pages. Based on the graph, which student fell short of the goal by the greatest number of pages, and by how many pages?
Answer: Dev by 20 pages
The question asks which student fell short of the 60-page goal by the most. From the bar graph, I calculate shortfalls: Alex read 50 (short by 10), Bri read 55 (short by 5), Chen read 65 (exceeded by 5), Dev read 40 (short by 20). Dev fell short by the greatest amount at 20 pages. Students often miscalculate by subtracting in the wrong order or missing that Chen exceeded the goal.
- A city recorded average monthly rainfall for the first half of the year. The line graph shows rainfall (in inches) for January through June. Which month had the greatest rainfall, and what was that value? Choose the option that matches both the correct month and the correct rainfall amount from the graph.
Answer: May, 4.1 inches
The question asks which month had the greatest rainfall and what that value was. Examining the line graph for January through June, the highest point occurs in May at 4.1 inches. Students must match both the correct month AND the correct value - a common error is identifying the right month but misreading the y-axis value.
- A lab measured the temperature of a solution as it cooled over time. The line graph shows temperature (in °C) at 0, 5, 10, 15, and 20 minutes. What is the average rate of change in temperature from 5 minutes to 15 minutes? Compute ΔtΔT using the values at those times.
Answer: −1.5 ∘C/min
The question asks for the average rate of temperature change from 5 to 15 minutes. From the graph, at 5 minutes the temperature is 25°C and at 15 minutes it's 10°C. The rate is (10 - 25)/(15 - 5) = -15/10 = -1.5°C/min. The negative sign indicates cooling, and students often forget to include it or mix up the order in the numerator. - A bar graph shows the number of hours four students studied for a test: Ava 6, Ben 4, Cara 7, Dan 5. According to the graph, how many more hours did Cara study than Ben?
Answer: 3 hours
The question asks for the difference in study hours between Cara and Ben. According to the graph, Cara studied 7 hours and Ben studied 4 hours. The difference is: 7 - 4 = 3 hours. A common error would be subtracting in the wrong order or reading the wrong students' values from the graph.
- A cafeteria tracked how many cartons of milk were sold each day. The line graph shows cartons sold from Day 1 to Day 7. On which day did sales first reach at least 90 cartons? Identify the earliest day whose plotted value is ≥90 using the y-axis scale.
Answer: Day 5
The question asks on which day milk sales first reached at least 90 cartons. Examining the line graph from Day 1 to Day 7, I need to find the first day where the value is ≥ 90. Day 5 is the first day showing a value at or above 90 cartons on the y-axis. Students often confuse "first reached" with "highest value" or misread the scale.
- A teacher compared the number of correct answers on a 20-question quiz across four class periods. The bar graph shows the class average (in questions correct) for Periods 1–4. What is the difference between the highest and lowest class averages? Use the exact bar heights to compute the spread.
Answer: 3 questions
The question asks for the difference between the highest and lowest class averages. From the bar graph, the highest average is Period 3 with 17 questions correct, and the lowest is Period 2 with 14 questions correct. The difference is 17 - 14 = 3 questions. Students often confuse finding the range with finding an average or misidentify which bars are highest and lowest.
- A farm tracked the price of apples per pound over five weeks. The line graph shows the price (in dollars) for Weeks 1–5. Over that period, the price decreased for some intervals and increased for others. Which statement is supported by the graph about the change from Week 2 to Week 4? Use the plotted values to determine the net change.
Answer: It increased by $0.10 per lb.
The question asks about the price change from Week 2 to Week 4. From the line graph, Week 2 shows $2.40 per pound and Week 4 shows $2.50 per pound. The change is $2.50 - $2.40 = $0.10 increase per pound. Students must be careful to subtract in the correct order and identify whether it's an increase or decrease.
- A line graph shows a car's distance from home (in miles) over time (in minutes). The graph gives: 0 min: 0 mi, 10 min: 6 mi, 20 min: 12 mi, 30 min: 12 mi, 40 min: 18 mi. During which 10-minute interval did the car travel the least distance?
Answer: 20–30 minutes
The question asks which 10-minute interval had the least distance traveled. Looking at each interval: 0-10 min: 6 miles, 10-20 min: 6 miles (12-6), 20-30 min: 0 miles (12-12, car stopped), 30-40 min: 6 miles (18-12). The 20-30 minute interval shows no change in distance, meaning the car traveled 0 miles. Common errors include miscalculating the distance for each interval or not recognizing that no change means zero distance traveled.
