Skip to main content
Sign in Create a free account
Varsity Tutors
Sign in

Interpret data from tables, charts, and graphs - TACHS Math

  1. Use the circle graph above to answer the question. The Ramirez family's monthly budget of $4,800 is divided among six categories as shown. If the family decides to transfer half of the amount spent on Entertainment into Savings, what will be the new ratio of Savings to Housing?
    Answer: 2 : 3 Read the percents from the circle graph: Housing 24%, Savings 8%, Entertainment 16%. With a budget of $4,800: Housing: 0.24 × $4,800 = $1,152. Entertainment: 0.16 × $4,800 = $768, and half of that is $384. Savings: 0.08 × $4,800 = $384. After the transfer, Savings is $384 + $384 = $768. The new ratio of Savings to Housing is 768 : 1,152. Both numbers divide by 384, giving 2 : 3. (In percents: 8% + 8% = 16% against 24%, and 16 : 24 = 2 : 3.) The ratio 1 : 3 is the original Savings to Housing, 8% : 24%, before any money moves. Moving all of Entertainment instead of half gives 24% : 24%, or 1 : 1. A ratio of 5 : 12 would need Savings to end at 10%, which does not match the graph. The new ratio of Savings to Housing is 2 : 3.
  2. Based on the dot plot below, what is the probability of rolling at least a 5 on this die experiment?
    Answer: 724\dfrac{7}{24} Dots: 1 (2), 2 (3), 3 (4), 4 (8), 5 (4), 6 (3). Total 24 trials. Rolls of 5 or 6 = 4+3=7, so probability 724\tfrac{7}{24}. Other fractions count wrong numbers of favorable outcomes.
  3. Refer to the double-bar graph. By how many books did 7th-grade girls exceed 7th-grade boys in January?
    Answer: 3 books The bars show 7th-grade girls read 14 books and boys read 11 books, a difference of 3. Other choices misread the graph or use other grades.
  4. Based on the line graph shown, during which month did the company experience the greatest decrease in profit compared to the previous month?
    Answer: From May to June The line drops $12 000\$12\,000 between May ($58 000\$58\,000) and June ($46 000\$46\,000), the largest single-month decline. Other intervals show smaller drops: Mar–Apr ($5k), Apr–May (rise), Jun–Jul ($4k).
  5. The box-and-whisker plots below compare the ages of members in Club A and Club B. Based on the plots, which statement must be true?
    Answer: At least 25% of Club A members are younger than at least 50% of Club B members. Club A: min 10, Q1 14, median 20, Q3 26, max 35. Club B: min 18, Q1 22, median 28, Q3 32, max 40. At least 25% of Club A (those below Q1=14) are younger than at least 50% of Club B (those below Q2=28). This must be true. A is about mean (can't determine from box plot). C: Club A range=25, Club B range=22, so C is false. D: Club A's median (20) is less than Club B's median (28), so less than half of Club A is above 28.
  6. Refer to the stacked bar chart below. Approximately what percent of students' after-school time was spent on homework?
    Answer: about 30% The homework segment occupies 3 hours out of a 10-hour total depicted, which is 30%. Other options misread the relative segment size.
  7. The histogram above shows the distribution of test scores for 50 students. Based on the histogram, what is the greatest possible value of the mean score?
    Answer: 80.6 To maximize the mean, assume every student scored at the top of their interval. Intervals and frequencies: 50-59 (5 students, max 59), 60-69 (10, max 69), 70-79 (15, max 79), 80-89 (12, max 89), 90-99 (8, max 99). Sum = 5(59)+10(69)+15(79)+12(89)+8(99) = 295+690+1185+1068+792 = 4030. Mean = 4030/50 = 80.6.
  8. The line graph above shows the temperature recorded every 2 hours during a 12-hour period. Based on the graph, during which 2-hour interval did the temperature change at the greatest rate (in absolute value)?
    Answer: From 6 PM to 8 PM From the graph: 8 AM→10 AM: 45°→52° (change 7). 12 PM→2 PM: 60°→68° (change 8). 2 PM→4 PM: 68°→72° (change 4). 6 PM→8 PM: 66°→54° (change -12). The greatest absolute change is 12°, from 6 PM to 8 PM.
  9. The graph below shows the distance (in miles) traveled by a cyclist as a function of time (in hours). According to the graph, during which period was the cyclist's average speed the greatest?
    Answer: From hour 3 to hour 4 Average speed = change in distance / change in time. 0→1 hr: 10 mi in 1 hr = 10 mph. 1→3 hr: 30-10=20 mi in 2 hr = 10 mph. 3→4 hr: 45-30=15 mi in 1 hr = 15 mph. 4→6 hr: 55-45=10 mi in 2 hr = 5 mph. Greatest average speed is 15 mph, from hour 3 to hour 4.
  10. The double bar graph shown below displays the number of books read by students in Mrs. Chen's class during the first and second semesters. Based on the graph, what was the percent increase in the total number of books read by all students combined from the first semester to the second semester?
    Answer: 33⅓% From the graph, first semester totals: 8+10+6+12+9 = 45 books. Second semester totals: 12+14+10+14+10 = 60 books. Percent increase = (60-45)/45 = 15/45 = 1/3 = 33⅓%. Choice A results from comparing 60 to 75 (wrong reference). Choice B uses (60-45)/50. Choice D uses (60-45)/37.5.
  11. Refer to the pie chart below. Which category represents exactly one-quarter of all responses?
    Answer: Basketball The chart shows Basketball occupying a 90° sector, which is 90360=14\frac{90}{360}=\frac{1}{4} of the circle. The other slices are 72° (Outdoor Soccer), 108° (Swimming), and 60° (Track & Field). Thus only Basketball is exactly one-quarter.
  12. The table below shows the number of hours that 4 employees worked each day during a 5-day week, along with their hourly wages. Based on the table, which employee earned the second-highest total weekly pay?
    Answer: Brianna Calculate total hours and weekly pay: Alex: 40 hours × $18 = $720. Brianna: 38 hours × $20 = $760. Carlos: 40 hours × $17 = $680. Diana: 35 hours × $22 = $770. Ranked by pay: Diana $770 (highest), Brianna $760 (second-highest), Alex $720, Carlos $680.
  13. Refer to the stem-and-leaf plot below showing the weights (in pounds) of 20 dogs at a shelter. What is the difference between the median weight and the mode of the weights?
    Answer: 3 pounds From the plot, the 20 weights in order are: 12, 15, 18, 19, 22, 25, 25, 27, 28, 31, 33, 35, 35, 35, 38, 42, 44, 45, 48, 51. Median = average of 10th and 11th values = (31+33)/2 = 32. Mode = 35 (appears three times). Difference = 35 - 32 = 3 pounds.
  14. The table below shows the populations (in thousands) of four cities in 2010 and 2020. Using the table, which city had the smallest percent change in population between 2010 and 2020?
    Answer: Camden Alton: (72-60)/60 = 20% increase. Baker: (100-120)/120 = -16.67% (decrease of ~16.7%). Camden: (85-80)/80 = 6.25% increase. Dover: (45-50)/50 = -10% (decrease of 10%). Smallest absolute percent change is Camden at 6.25%. Choice A has largest change. Choices B and D are larger decreases than Camden's increase.
  15. Use the Venn diagram to determine how many students take piano lessons only (not violin).
    Answer: 6 students Piano circle shows 6 in the piano-only region, 4 in the overlap, violin-only region has 9. Thus 6 piano-only. Other choices mix regions or totals.
  16. The two-way frequency table shown displays the transportation method used by students in two grades. Refer to the table. What percent of 7th graders walk to school, rounded to the nearest whole percent?
    Answer: 18% From the table: 7th graders total = 28+45+22+30 = 125. 7th graders who walk = 22. Percent = 22/125 = 0.176 = 17.6% ≈ 18%. Choice A divides walkers (22) by total students ignoring other grade. Choice C is 22/110. Choice D is 30/125 (wrong row).
  17. The table below shows the scores of 5 students on 4 quizzes. According to the table, which student has the greatest difference between their mean score and their median score?
    Answer: Student Y Student W: scores 80,82,84,86 → mean 83, median 83, diff 0. Student X: 70,75,80,95 → mean 80, median 77.5, diff 2.5. Student Y: 60,90,92,94 → mean 84, median 91, diff 7. Student Z: 85,85,90,100 → mean 90, median 87.5, diff 2.5. Student Y has the greatest difference.
  18. Use the histogram below to determine the median test score for the class.
    Answer: 82 There are 30 students. Cumulative frequencies: 70-74 (3), 75-79 (7), 80-84 (16), 85-89 (25), 90-94 (30). The 15th and 16th scores fall in 80-84, so the median is in that bin; choosing the midpoint gives 82. Choices A and C fall on bin edges, D is in a higher bin.
  19. The Venn diagram above shows the number of students in a school of 200 who play Soccer (S), Basketball (B), and Tennis (T). Based on the diagram, what is the probability that a randomly chosen student plays exactly one of the three sports?
    Answer: 47100\frac{47}{100} Students playing exactly one sport: Only S = 35, Only B = 40, Only T = 19. Sum = 94. Probability = 94/200 = 47/100. Choice B includes two-sport overlaps. Choice C includes all who play at least one. Choice D excludes Tennis-only.

Start this quiz