Interpreting & Synthesizing Data in Graphs and Tables – Problem Solving & Data Analysis (Calculator) for the SAT
In the SAT Math section, particularly the Problem Solving and Data Analysis domain, a key skill is the ability to interpret, analyze, and synthesize information presented in various graphical or tabular formats. This might include bar graphs, line graphs, scatterplots, pie charts, box-and-whisker plots, two-way tables, and more. Examining these visual representations of data accurately and efficiently is crucial for answering questions about rates, proportions, correlations, mean/median calculations, trends, and predictions.
Below, you will find 50 practice questions that replicate the types of data interpretation tasks you may encounter in the SAT’s calculator-allowed portion. Each question is accompanied by a thorough solution that shows step-by-step reasoning, offering insights into best strategies for reading the data, isolating relevant points, performing the necessary calculations, and synthesizing the findings to make accurate conclusions.
These practice items cover a wide range of scenarios: analyzing sales data in a table, deducing growth patterns from a line chart, dissecting demographic information in a bar graph, computing averages and standard deviations, employing percentages from a circle graph, and examining two-variable data to identify linear or non-linear relationships. In many questions, you will also find word-problem contexts that require transferring the numeric or graphical information into well-grounded conclusions or additional computations.
We hope these questions strengthen your confidence and capacity to tackle data-intensive questions under time constraints. Be sure to practice not only the calculation aspect, but also your skill in quickly reading and comprehending the data. Familiarizing yourself with common traps (like incorrectly reading scales, misinterpreting intervals, or skipping important notes in the figure legends) will help you avoid costly mistakes. With consistent practice, you’ll be well-equipped to excel in the SAT’s Problem Solving and Data Analysis tasks.
Question 1
A bar graph displays the number of students who opted for various extracurricular activities: Music, Sports, Art, and Debate. The bars read as follows: Music – 40 students, Sports – 60 students, Art – 25 students, Debate – 35 students. If the total school enrollment is 200 students, what fraction of the student body does each activity represent? Express each fraction in simplest form.
Solution
The bar graph indicates the following counts:
- Music: 40 students
- Sports: 60 students
- Art: 25 students
- Debate: 35 students
Total = 200 students.
For each activity, we find the fraction of the total 200:
- Music: \( \frac{40}{200} = \frac{1}{5} \).
- Sports: \( \frac{60}{200} = \frac{3}{10} \).
- Art: \( \frac{25}{200} = \frac{1}{8} \) (since 25/200 = 1/8).
- Debate: \( \frac{35}{200} = \frac{7}{40} \) (divide numerator and denominator by 5).
Therefore, the fractions are:
- Music: \( \frac{1}{5} \)
- Sports: \( \frac{3}{10} \)
- Art: \( \frac{1}{8} \)
- Debate: \( \frac{7}{40} \)
Question 2
A two-way table shows how 100 survey respondents answered two yes/no questions (Q1 and Q2). The table is as follows:
Q2: Yes Q2: No Row Totals
Q1: Yes 30 20 50
Q1: No 15 35 50
Column Tots 45 55 100
(a) What fraction of the respondents answered Yes to both Q1 and Q2?
(b) Among those who answered Yes to Q1, what fraction also answered Yes to Q2?
(c) Among those who answered No to Q1, what fraction answered No to Q2?
Solution
(a) The number who answered Yes to both Q1 and Q2 is 30. There are 100 total respondents, so the fraction is \( \frac{30}{100} = \frac{3}{10}. \)
(b) Among the 50 who answered Yes to Q1 (from the row total), 30 said Yes to Q2. So that fraction is \( \frac{30}{50} = \frac{3}{5}. \)
(c) Among those who answered No to Q1, the row total is 50, and 35 of those answered No to Q2. The fraction is \( \frac{35}{50} = \frac{7}{10}. \)
Question 3
A line graph tracks the daily high temperatures over a week, in degrees Fahrenheit: Day 1: 70°F, Day 2: 73°F, Day 3: 72°F, Day 4: 68°F, Day 5: 74°F, Day 6: 75°F, Day 7: 71°F. What is the mean daily high temperature over this 7-day period? Round to the nearest tenth if necessary.
Solution
Sum the given temperatures:
70 + 73 + 72 + 68 + 74 + 75 + 71 = 503.
Since there are 7 days, the mean is \( 503 ÷ 7 \approx 71.857. \) Rounded to the nearest tenth: 71.9°F.
Question 4
A circle graph (pie chart) breaks down the distribution of 500 employees across 5 departments in a company. The chart shows:
- Marketing: 25%
- Sales: 15%
- Development: 40%
- HR: 10%
- Finance: 10%
How many employees are in each department?
Solution
We have 500 total employees. The percentage distribution is:
- Marketing: 25% of 500 => 0.25 × 500 = 125
- Sales: 15% of 500 => 0.15 × 500 = 75
- Development: 40% => 0.40 × 500 = 200
- HR: 10% => 0.10 × 500 = 50
- Finance: 10% => 0.10 × 500 = 50
Check the total: 125 + 75 + 200 + 50 + 50 = 500, which matches the total employee count.
Question 5
A table of monthly rainfall (in inches) for a certain city reads: Jan: 3.2, Feb: 2.8, Mar: 3.5, Apr: 4.2, May: 3.8, Jun: 2.0. If the question asks for the total rainfall for the first half of the year (Jan–Jun), and the average monthly rainfall over these six months, what are these two values?
Solution
Sum the rainfall from January to June:
3.2 + 2.8 + 3.5 + 4.2 + 3.8 + 2.0 = 19.5 inches total.
The average monthly rainfall over these six months is \( 19.5 ÷ 6 ≈ 3.25 \) inches per month.
Answer: Total = 19.5 inches, average = 3.25 inches/month.
Question 6
A scatterplot shows the relationship between students’ hours of test preparation (x-axis) and their test scores (y-axis) for 10 students. The scatterplot suggests a positive linear trend with a correlation coefficient of approximately r = 0.85. If one student studied 6 hours but had an outlier score that is much lower than the trend, how would removing this point likely affect the correlation coefficient?
Solution
A positive correlation of 0.85 indicates a strong linear relationship. The described outlier is well below the main trend for 6 hours of study. Removing a low outlier that disrupts an otherwise stronger positive pattern typically increases the correlation coefficient, because the data will align more closely with the best-fit line once the outlier is removed.
Answer: Removing the outlier will likely increase the correlation from 0.85 to something higher, as the fit becomes tighter.
Question 7
A bar chart compares five different fruit smoothie flavors sold in a week: Strawberry (80 units), Mango (65 units), Banana (50 units), Mixed Berry (70 units), and Watermelon (35 units). How many total smoothies were sold, and what percent of the total did the Strawberry flavor account for?
Solution
Sum up all the units sold:
80 (Strawberry) + 65 (Mango) + 50 (Banana) + 70 (Mixed Berry) + 35 (Watermelon) = 300 total smoothies.
The strawberry flavor is 80 out of 300. The percentage is \( \frac{80}{300} × 100\% ≈ 26.67\%. \)
Answer: 300 total smoothies; Strawberry is ~26.7% of total.
Question 8
A table lists the average SAT Math scores for a sample of 5 states:
State A: 550
State B: 580
State C: 560
State D: 570
State E: 585
If each state sample has 1,000 test-takers, what is the overall average SAT Math score across all 5,000 students combined?
Solution
If each state has 1,000 test-takers, the total is 5,000 test-takers. We can find the weighted average (though each has the same weight, 1,000 students).
Sum the average scores (multiplied by 1,000 each):
- State A: 550 × 1000 = 550,000
- State B: 580 × 1000 = 580,000
- State C: 560 × 1000 = 560,000
- State D: 570 × 1000 = 570,000
- State E: 585 × 1000 = 585,000
Sum: 550,000 + 580,000 + 560,000 + 570,000 + 585,000 = 2,845,000 total points. Divide by 5,000 students: \[ \frac{2,845,000}{5,000} = 569. \]
Answer: The overall average across all five states is 569.
Question 9
A line graph shows a company's monthly revenue from January to June in increments of $1000: Jan: \$20k, Feb: \$22k, Mar: \$25k, Apr: \$23k, May: \$26k, Jun: \$28k. By how much did the revenue change from January to June, and what is the percent increase over that time?
Solution
January’s revenue: \$20k. June’s revenue: \$28k.
Change = \$28k – \$20k = \$8k.
The percent increase from January to June is \( \frac{\$8k}{\$20k} × 100\% = 40\%. \)
Answer: The revenue rose by \$8k, which is a 40% increase.
Question 10
A stacked bar chart shows the composition of a certain product's material costs. The product total cost is \$100. Of that, \$40 is electronics, \$30 is plastic casing, and \$15 is packaging, with the remainder being labor costs. According to the chart, what fraction of the total is spent on labor costs?
Solution
The sum of the given amounts is \$40 (electronics) + \$30 (plastic) + \$15 (packaging) = \$85. The total cost is \$100, so the labor portion is \$100 – \$85 = \$15.
The fraction is \( \frac{15}{100} = \frac{3}{20}. \)
Answer: \(\frac{3}{20}\) of the total cost is labor, which is 15%.
Question 11
A dot plot shows the distribution of exam scores for a class of 10 students:
Scores: 72, 74, 74, 75, 78, 78, 78, 80, 90, 96.
(a) What is the median score?
(b) If a new student joins the class with a score of 76, how does that affect the median?
Solution
(a) With 10 students, the median is the average of the 5th and 6th highest scores when the data is sorted. In sorted order, the 5th score is 78, the 6th score is also 78. The median is \(\frac{78+78}{2}=78.\)
(b) Now there are 11 scores, which is an odd count. We list them: 72, 74, 74, 75, 76 (new student), 78, 78, 78, 80, 90, 96. The median is now the 6th score (since for 11 data points, median is the (n+1)/2 = 6th). The 6th score is 78.
So the median remains 78, unchanged.
Question 12
The following box-and-whisker plot summarizes test scores out of 100 for a group of students:
- Minimum: 65
- Q1: 72
- Median: 80
- Q3: 88
- Maximum: 95
What is the interquartile range, and how many students scored below 72 if there are 40 students total (assuming a uniform distribution within quartiles is not always correct, but typically the box-and-whisker representation suggests Q1 has 25% of data below it)?
Solution
The interquartile range (IQR) is Q3 - Q1 = 88 - 72 = 16.
By definition, Q1 is the 25th percentile, meaning 25% of the observations lie below 72. If there are 40 students, then 25% of 40 is 10. So 10 students scored below 72.
Question 13
A research chart indicates the heights (in inches) of 5 plants at the end of each week for 4 weeks. The data for one plant, Plant A, is:
Week 1: 6 in, Week 2: 9 in, Week 3: 11 in, Week 4: 14 in.
(a) What is the average growth per week from Week 1 to Week 4 for Plant A?
(b) If the bar representing Plant A in a grouped bar chart for Week 4 is 14 in tall, while the scale on the y-axis is 1 inch per 5 units, how tall is that bar in actual chart units?
Solution
(a) Plant A’s height goes from 6 inches in Week 1 to 14 inches in Week 4. That’s a growth of 14 - 6 = 8 inches over 3 intervals (Week 1 to 2, 2 to 3, 3 to 4). Another approach: the difference is 8 inches from the start of Week 1 to the end of Week 4. That’s over 3 weeks if counting from the end of Week 1 to the end of Week 4. Usually, we might say it’s an average of 8/3 = 2.67 inches per week if we interpret it as 3 intervals.
If we interpret “from Week 1 to Week 4” as 3 increments, the average growth is 2.67 in/week. If we consider an alternative (the full 4 weeks), that might be 8/4 = 2 in/week, but typically you measure intervals from one reading to the next, so 2.67 in/week is the standard approach.
(b) If the scale is 1 inch in the chart per 5 actual units, then for 14 units (inches of plant height), the bar is \( \frac{14}{5} \) inches tall on the chart, which is 2.8 inches on the chart.
Question 14
A pie chart compares the market shares of 4 smartphone brands in percentages: A (30%), B (25%), C (25%), D (20%). If the chart indicates brand B's slice is 25%, and 25% corresponds to 50 million units sold, how many total units are sold in the smartphone market across all brands?
Solution
If brand B’s 25% equals 50 million units, that means 25% → 50 million. So 1% → 2 million. Therefore 100% → 200 million total units in the market.
Answer: 200 million units total across all brands.
Question 15
A frequency table of test scores (70–74, 75–79, 80–84, 85–89, 90–94, 95–99) is displayed. Suppose the table is:
70–74: 5 students
75–79: 8 students
80–84: 10 students
85–89: 12 students
90–94: 6 students
95–99: 4 students
(a) How many students are there total?
(b) What fraction of students scored 85 or above?
Solution
(a) Total = 5 + 8 + 10 + 12 + 6 + 4 = 45 students.
(b) Those who scored 85 or above are in the last three classes: 12 + 6 + 4 = 22. The fraction is \(\frac{22}{45}.\)
Question 16
A histogram depicts the distribution of weights (in pounds) of 40 packages. The largest bin interval on the histogram is 30–34 lb, with a frequency of 12. If the next largest bin is 35–39 lb with frequency 10, what is the total number of packages that weigh at least 30 lb, according to the histogram?
Solution
The question is specifically about the total number of packages that weigh at least 30 lb. The bin 30–34 lb has 12 packages, and the bin 35–39 lb has 10 packages. Possibly there might be heavier bins beyond 35–39 lb, but let's assume these are the only bins at or above 30 lb. Then the total is 12 + 10 = 22 packages.
Answer: 22 packages weigh at least 30 lb.
Question 17
A table of average gas prices (in \$ per gallon) for each quarter of the year is shown:
Q1: \$2.80
Q2: \$3.10
Q3: \$3.00
Q4: \$3.20
Over the full year, what is the average price? Also find the approximate percent increase from Q1 to Q4.
Solution
Average across 4 quarters: \[ \frac{2.80 + 3.10 + 3.00 + 3.20}{4} = \frac{12.10}{4} = 3.025. \] So \$3.03 per gallon, approximately.
From Q1 (\$2.80) to Q4 (\$3.20), the change is \$0.40. The percent increase is \( \frac{0.40}{2.80} × 100\% ≈ 14.3\%. \)
Question 18
A stacked column chart compares two categories, men and women, across four different age brackets. In the 20–29 bracket, the chart shows men’s bar segment as 30, women’s segment as 50, for a total of 80. If we are told that the chart’s data reflect thousands of individuals, how many individuals in total are in the 20–29 bracket, and what fraction are men?
Solution
The chart shows men = 30, women = 50, total 80 for that bracket. Since each unit is in thousands, that means 80,000 total in 20–29 bracket, of whom 30,000 are men.
The fraction men is \( \frac{30,000}{80,000} = \frac{3}{8} = 0.375. \)
Answer: 80,000 total in 20–29 bracket, fraction men = 3/8.
Question 19
The following side-by-side bar graph compares annual incomes for 3 different professions (A, B, C) over 2 years (Year 1, Year 2). The bars for Year 1 are: A = \$40k, B = \$42k, C = \$39k. The bars for Year 2 are: A = \$43k, B = \$45k, C = \$41k. For each profession, find the percent increase from Year 1 to Year 2.
Solution
Let’s compute each:
- Profession A: From \$40k to \$43k, increase = \$3k. % increase = (3 / 40) × 100% = 7.5%.
- Profession B: From \$42k to \$45k, increase = \$3k. % increase = (3 / 42) × 100% ≈ 7.14%.
- Profession C: From \$39k to \$41k, increase = \$2k. % increase = (2 / 39) × 100% ≈ 5.13%.
Question 20
A table lists the number of units sold per quarter for 2 products:
Product X: Q1=500, Q2=600, Q3=550, Q4=650.
Product Y: Q1=400, Q2=450, Q3=500, Q4=600.
For each product, find the total annual units sold. Also, which product has a higher average quarterly sales figure?
Solution
For Product X: 500 + 600 + 550 + 650 = 2,300 units in total.
For Product Y: 400 + 450 + 500 + 600 = 1,950 units total.
Average for X = 2,300 ÷ 4 = 575 units/quarter.
Average for Y = 1,950 ÷ 4 = 487.5 units/quarter.
Product X has the higher average (575 vs 487.5).
Question 21
A circle graph breaks down the distribution of votes among four candidates (W, X, Y, Z). The chart indicates: W=10%, X=25%, Y=30%, Z=35%. If the total votes are 800, how many votes did each candidate receive, and which candidate is the winner?
Solution
Multiply each percentage by 800:
- W: 0.10 × 800 = 80
- X: 0.25 × 800 = 200
- Y: 0.30 × 800 = 240
- Z: 0.35 × 800 = 280
Z has 280 votes, the largest. Hence, candidate Z is the winner.
Question 22
A line chart shows the daily production of a factory (in units) for 5 days: Mon=200, Tue=220, Wed=230, Thu=210, Fri=250. What is the overall range (difference between max and min) of daily production, and on which day was the production the highest?
Solution
The minimum production is 200 (Monday), the maximum is 250 (Friday). Range = 250 - 200 = 50.
The highest daily production is on Friday at 250 units.
Question 23
A side-by-side bar graph compares the monthly rainfall of two cities (A and B) for 3 months (Jan, Feb, Mar). The data:
City A: Jan=3 in, Feb=4 in, Mar=5 in
City B: Jan=2 in, Feb=3 in, Mar=7 in
Which city has a higher total rainfall for the 3-month period, and by how many inches?
Solution
Sum for City A: 3 + 4 + 5 = 12 inches total.
Sum for City B: 2 + 3 + 7 = 12 inches total.
They both sum to 12 inches. So neither has more; the difference is 0.
Question 24
A table of random sample data shows the distribution of a certain characteristic among 200 individuals. Suppose 80 are classified as Type 1, 60 as Type 2, and 60 as Type 3. If a pie chart is created, what is the angle measure of the sector for Type 1 in the chart?
Solution
Type 1 has 80 out of 200 total, or 40% of the sample. A full circle is 360°. 40% of 360° is 0.40 × 360 = 144°.
Answer: The sector angle is 144°.
Question 25
A box-and-whisker plot for a data set shows the following 5-number summary: min=20, Q1=30, median=40, Q3=45, max=60. If there are 40 observations total, how many data points lie in the interval between Q1 and Q3, inclusive?
Solution
Q1 to Q3 typically captures the middle 50% of the data in a box-and-whisker representation. 50% of 40 is 20. So 20 data points lie in [Q1, Q3], inclusive.
Question 26
A frequency polygon shows the distribution of times (in minutes) it takes 50 students to complete a puzzle. The peak of the polygon is at the 10–12 minute bin with a frequency of 15. Another bin (13–15 min) has frequency 12. If we combine these two adjacent bins, what is the total frequency for the combined 10–15 minute range?
Solution
The bin 10–12 minute has 15, 13–15 minute has 12. Combining them is 15 + 12 = 27.
Answer: The combined frequency is 27.
Question 27
A scatterplot of x=hours studied vs y=exam score shows a roughly linear upward trend. If the correlation coefficient r=0.65, which statement is most appropriate:
(A) There's a strong linear correlation.
(B) There's a moderate positive correlation.
(C) There's a weak positive correlation.
(D) There's no correlation.
Solution
A correlation of 0.65 is typically considered moderate to moderately strong. 0.65 is not so high as 0.9 or so. So the best descriptor is “moderate positive correlation.”
Answer: (B) There's a moderate positive correlation.
Question 28
A line graph compares the average daily steps of a person over 7 consecutive days. The data: 8,000 on Day 1, 10,000 on Day 2, 12,000 on Day 3, 7,500 on Day 4, 9,500 on Day 5, 10,500 on Day 6, 11,000 on Day 7. By how much did the highest day exceed the lowest day?
Solution
Highest day is Day 3 with 12,000 steps. The lowest day is Day 4 with 7,500 steps. The difference = 12,000 - 7,500 = 4,500 steps.
Question 29
A histogram of salaries (in thousands of dollars) for 50 employees is right-skewed. The table below shows the median is \$55k, the mean is \$60k, and the mode is \$50k. Which is the largest measure of center for a right-skewed distribution, typically, and does the data reflect that pattern?
Solution
In a right-skewed distribution, the mean is typically the largest measure of center, followed by the median, then the mode. Here, the mode is 50, median is 55, mean is 60, which follows the typical pattern (mode < median < mean). So yes, the data does reflect that pattern for a right-skewed distribution.
Question 30
A bar chart shows the counts of five categories: Category 1=10, Category 2=15, Category 3=20, Category 4=15, Category 5=40. If we combine Categories 3 and 5 into a single new category, how many items does that new category have, and what fraction of the total does it represent?
Solution
Category 3 has 20, Category 5 has 40. Combined is 60.
The total original set is 10 + 15 + 20 + 15 + 40 = 100.
The new category’s fraction is \( \frac{60}{100} = \frac{3}{5} \).
Question 31
A line graph shows the monthly number of website visitors (in thousands) for 4 months: M1=20, M2=24, M3=30, M4=28. If each point on the graph is connected by straight segments, what is the net change from M1 to M4, and which month had the largest single increase from the previous month?
Solution
M1=20, M4=28 => net change is +8 thousand.
The increments are: M1->M2 = +4, M2->M3 = +6, M3->M4 = -2. The largest single increase is +6 from M2 to M3.
Answer: Net change = +8k. Largest jump is M2->M3 (+6k).
Question 32
A two-way table tracks the presence/absence of a certain trait among 200 individuals, half male, half female. If 60 out of the 100 males have the trait, and 50 out of the 100 females have the trait, what is the overall proportion that have the trait?
Solution
Males with trait: 60, Females with trait: 50, total with trait = 110 out of 200. The proportion is \( \frac{110}{200} = 0.55 = 55\%. \)
Question 33
A table lists the daily sales (in \$) for a store over 7 days: 1200, 1300, 1500, 900, 1100, 2000, 1800. (a) What is the mean daily sales figure? (b) On a line chart with a y-axis scale of 1 vertical inch per \$500, how tall would the bar (or point) for 2000 be in chart inches?
Solution
(a) Sum: 1200 + 1300 + 1500 + 900 + 1100 + 2000 + 1800 = 9800. The mean is \( 9800 / 7 ≈ 1400. \)
(b) If 1 vertical inch = \$500, then for \$2000, we have \( 2000 / 500 = 4 \) inches on the chart.
Question 34
A scatterplot suggests a weak negative association between x and y variables. The correlation coefficient is about r = -0.2. If a new data point is introduced that fits the negative trend more strongly, how might r be affected?
Solution
A new point that further aligns with a negative trend (i.e., consistent with a negative slope) likely makes the relationship more pronounced, so the correlation coefficient might become more negative. That is, it might move from -0.2 to, say, -0.3 or lower in that direction.
Question 35
A stacked bar chart compares the revenue from 3 product lines (P1, P2, P3) over 2 different years. The Year 1 stack is: P1=\$10k, P2=\$20k, P3=\$15k. The Year 2 stack is: P1=\$12k, P2=\$25k, P3=\$18k. (a) What is total revenue each year? (b) Which product line had the largest absolute increase from Year 1 to Year 2?
Solution
(a) Year 1 total: 10k + 20k + 15k = \$45k. Year 2 total: 12k + 25k + 18k = \$55k.
(b) The changes are: P1 +2k, P2 +5k, P3 +3k. The largest is P2 at +5k.
Question 36
A circle graph shows the distribution of 600 members among 6 committees, each committee occupying an equal slice. If the chart is indeed evenly split, how many members does each committee have, and what is the central angle for each sector?
Solution
If it’s evenly split 6 ways, each committee is 600 ÷ 6 = 100 members.
Each slice is 360° ÷ 6 = 60° in the pie chart.
Question 37
A box-and-whisker plot for 20 data points has Q1=40 and Q3=50, with an IQR=10. If the median is 45, is it guaranteed that exactly 10 data points fall within 40–50? Explain.
Solution
Typically, Q1 and Q3 define the middle 50% of data. However, with only 20 data points, the distribution of data points within each quartile can vary slightly. Usually, we say about 50% lie in the IQR. But exactness can be tricky with discrete data. So, it’s not guaranteed exactly 10 data points lie in [40,50], but it’s typically around half. The quartiles are boundaries for 25% and 75% positions in sorted data, so we expect ~50% within Q1–Q3, but the discrete nature might cause some mild variation.
Question 38
A frequency table shows the number of books read by each of 50 students in a summer reading program. If the average (mean) number of books read is 4.2, estimate the total number of books read by all 50 students, and interpret that in the context of a bar chart that might be used to represent these data.
Solution
The average is 4.2 books per student. With 50 students, total books read is 4.2 × 50 = 210.
In a bar chart for the distribution, the total area under the bars (when we sum frequencies × their respective book counts) would be 210 total books.
Question 39
A histogram groups test scores (out of 100) in intervals of width 5. The highest frequency is in the 80–84 range (12 students). Another question states that 40% of the class scored 80 or above. If there are 50 students total, how many scored below 80?
Solution
If 40% scored 80 or above, that’s 0.40 × 50 = 20. So the number who scored below 80 is 50 - 20 = 30.
Question 40
A side-by-side bar chart compares the pass rates for two sections of a course across 3 semesters: The pass rates for Section 1 are 85%, 88%, 90%, while for Section 2 they are 80%, 82%, 88%. If each bar represents a pass rate as a fraction of 1, which section consistently has the higher rate?
Solution
Compare each semester:
- Semester 1: Section 1=85%, Section 2=80% => S1 is higher.
- Semester 2: Section 1=88%, Section 2=82% => S1 is higher.
- Semester 3: Section 1=90%, Section 2=88% => S1 is higher.
So Section 1 consistently has the higher pass rate.
Question 41
A table shows the number of goods produced by 4 machines (A,B,C,D) in one hour: 120, 150, 100, 130, respectively. If the question asks which machine is most productive, what is the direct interpretation from the table?
Solution
The machine with the largest output is B with 150 units. That straightforwardly indicates B is the most productive within that one-hour snapshot.
Question 42
A line chart tracks the membership count of a gym over 5 years: Year 1=300, Year 2=350, Year 3=400, Year 4=450, Year 5=470. (a) What is the overall growth from Year 1 to Year 5? (b) Which two-year interval shows the largest jump?
Solution
(a) 470 - 300 = 170 net growth in membership.
(b) The increments each year: Y1->Y2=+50, Y2->Y3=+50, Y3->Y4=+50, Y4->Y5=+20. The largest jump is +50, happening in intervals Y1->Y2, Y2->Y3, and Y3->Y4 (all tied).
Question 43
A bar chart of 4 categories shows category frequencies: 12, 18, 20, and 30. If we want to find the mode from this bar chart, which category is the mode, and how do we identify it?
Solution
The mode is the category with the highest frequency. The frequencies are 12, 18, 20, and 30. The highest is 30, so that category is the mode. We identify it by seeing which bar is tallest in the bar chart.
Question 44
A scatterplot of x=years after 2000 vs y=population (thousands) shows an exponential curve. If in 2000 the population was 50k and in 2010 it was 100k, how does that reflect in the data plot from x=0 to x=10? Also, what is the approximate growth factor if it doubled over 10 years?
Solution
The point at x=0 (year 2000) is y=50. The point at x=10 (year 2010) is y=100. This suggests the population doubled in that decade, consistent with an exponential growth shape. The growth factor over 10 years is 2. For an annual factor, we might approximate the 10th root of 2, which is about 1.07 per year. But the question specifically: The growth factor for the entire period is 2.
Question 45
A circle graph shows how 200 hours of volunteer work are divided among four tasks (T1, T2, T3, T4). The slice for T3 is 72°, and the total circle is 360°. How many hours were spent on T3?
Solution
T3’s slice is 72° out of 360°, which is 72/360 = 1/5 of the total. 1/5 of 200 hours is 40 hours.
Question 46
A table of average daily temperatures (in °C) for 5 days is: 18, 20, 19, 15, 21. If a line chart is drawn, which day’s temperature is the minimum, and by how many degrees is it below the average of these 5 days?
Solution
The minimum temperature is on day 4 at 15°C. The mean of 5 days is (18+20+19+15+21)=93, 93/5=18.6. The difference from 15°C is 3.6°C below average.
Question 47
A side-by-side bar chart shows product sales for two regions (Region X and Region Y) across 3 months. The data:
Region X: M1=100, M2=120, M3=110
Region Y: M1=90, M2=130, M3=115
Which region has the higher total across all 3 months, and by how much?
Solution
Sum Region X: 100+120+110=330. Sum Region Y: 90+130+115=335.
Region Y is higher by 5 (335–330=5).
Question 48
A scatterplot with a regression line is shown for heights (x) vs weights (y) of 30 individuals. The equation of the best-fit line is y=3x–100, and the correlation is r=0.75. If someone has x=60 inches in height, the line predicts y=80 pounds. If the actual data point is (60,90), what is the residual for that point?
Solution
The predicted weight from the line is 80 at x=60. The actual weight is 90. Residual= actual - predicted= 90-80= +10. So the data point is 10 above the regression line's prediction.
Question 49
A line chart plots the cumulative sales for a product from Jan to Jun. The chart shows: Jan=\$10k, Feb=\$18k, Mar=\$25k, Apr=\$30k, May=\$35k, Jun=\$40k. How many new sales occurred between April and June?
Solution
Because it’s cumulative, the total in April is \$30k, by June it’s \$40k. So the new sales from Apr to Jun is \$40k - \$30k= \$10k.
Question 50
A two-way table for 300 participants in a study shows:
- Group A (150 participants): 90 prefer Option 1, 60 prefer Option 2.
- Group B (150 participants): 70 prefer Option 1, 80 prefer Option 2.
(a) Among Group A, what fraction prefer Option 1?
(b) Across the entire 300 participants, how many prefer Option 2?
Solution
(a) In Group A, 90 out of 150 choose Option 1, that’s 90/150=3/5=0.6.
(b) The total who prefer Option 2 is 60 in Group A plus 80 in Group B=140 participants.
Conclusion and Final Tips
By working through these 50 practice questions, you have seen how to extract information from a range of graphical and tabular data representations—bar charts, line graphs, circle graphs, box plots, scatterplots, and two-way tables. Key takeaways include:
- Careful Reading of Labels: Always check scales, units, intervals, and categories. Misreading a scale or ignoring a “per 1000” note can lead to incorrect answers.
- Performing Correct Calculations: Whether you’re finding the mean, median, fraction of a whole, or percent change, double-check your arithmetic. On the SAT, small errors can cost valuable points.
- Synthesizing Information: You may need to combine data from multiple bars or intervals, interpret differences in distributions, or compare categories across multiple dimensions (like a stacked bar or a two-way table).
- Recognizing Trends: In line graphs or scatterplots, pay attention to increases vs. decreases, approximate slopes, correlation coefficients, and potential outliers. Correlation does not imply causation, but you should identify the sign and approximate strength of a correlation if needed.
- Check Reasonableness: After obtaining a number or a fraction, verify if it makes sense in context. For instance, if the fraction surpasses 1 or the sum of segments in a circle graph isn’t 100%, you likely made a mistake.
Consistent practice interpreting data from graphs and tables will make you more proficient and confident under timed test conditions. Keep honing these skills, and you’ll be well prepared for the Problem Solving and Data Analysis portion of the SAT Math section.
