Graphs and Tables - SAT Math

The key to any graph-based question is to make sure to look not just at the graph itself, but also at any additional information that is presented with the graph. In this case, you are told that the bars on the left represent how the scientists would view others' future work if the other person admitted to wrongdoing. Notice that if the other person admitted that they had been wrong that the people surveyed would be less likely to suspect them than if they didn't admit to wrongdoing. In contrast, the bars on the right show how they would anticipate others to react if they admitted to wrongdoing. In this case, they said that others would be more suspicious of their work if they did admit to wrongdoing than if they didn't. The answer that matches this is "incorrectly assumed that admitting that a study was wrong would lead others to be more suspicious of their work". While they assumed that others would be more suspicious of their work if they admitted to wrongdoing, scientists, in general, were less suspicious of individuals who admitted to wrongdoing.

Scientists viewed others who admitted to wrongdoing with less suspicion than they viewed people who did not admit to wrongdoing. However, scientists believed that others would view them as less trustworthy if they admitted to wrongdoing. This matches "scientists believed that others would view them as much less honest if they admitted to wrongness."

The other choices can all be eliminated because they make the claim that there is some sort of relationship that can be drawn between scientists in one group and the other. Because you don't have scientist- by-scientist data, however, you can't make any conclusions linking individual scientists in each survey group.

When breaking down graphs and tables, it’s important to pay close attention to often overlooked details such as scale, labels, and titles. Here, we’re told what this pie graph is measuring right in the title - it’s a graph of world landmass by continent. We can do the math to identify that “Asia is approximately 50% larger, based on landmass than Africa,” that “The landmass of Africa is approximately the same size as the combined landmass of Antarctica, Europe, and Australia,” and that “The two Americas account for a combined 29% of the world’s landmass.” However, we do not know that “Half of the earth’s surface area is covered by Asia and Africa.” If we attempt to draw this conclusion, we’ve made a critical mistake in reading - we’ve forgotten about the water! There’s a drastic difference between “world landmass” and “world surface area,” since the former is looking only to the land, and the latter includes all surface area, even the portion covered by the deep blue! It’s critical that we pay close attention to what the data is measuring when interpreting graphs and tables, because convincing wrong answers - and in this case, our answer to an “except” question - will often draw us in with options that sound on-topic but address different data from the data we were presented within the figure.

When breaking down graphs and tables, it’s important to pay close attention to often overlooked details such as scale, labels, and titles. Here, the bar graph we’ve been given represents undergraduate enrollment. So, we can only feasibly draw conclusions about the enrollment of the schools in question. So, answers that address graduation rates or compare them cannot be concluded based on the bar graph alone. Only our correct answer “The total enrollment for Ivy League schools in 2010 was greater than 40,000 students,” can be confidently concluded based on the information, and we can get there efficiently using rounding and estimation, as the total is well over the 40,000 mark.

In this example, we can use process of elimination and a bit of rounding to arrive at our correct answer efficiently. We can conclude that the sample’s total hours worked per month did not increase each month from January to December, or even from January to July, as there is a clear decrease from February to March, as well as several more decreases later in the year. We also cannot conclude that hours worked decreased each month from July to December, as we can see a clear increase from October to November, and again from November to December. We can, however, conclude that “The sample’s total hours worked in May through August were greater than the total hours worked for the rest of the year.” Even if we apply a bit of rounding, the roughly 15+20+40+36 gives us around 110 for the months in question. (and yes, we’d want to keep in mind that these are weekly figures and that the *actual* values would depend on the weeks in the month and the number of participants in the sample group. That said, this change will be proportional, so we can simplify by looking to the weekly and average amounts.) This roughly 110 far surpasses the sum for the remainder of the months, even if we round up, as most are at or below roughly 10. Keep in mind, graph questions on the SAT are never meant to be an eye exam - so if it seems as though the numbers are “too close to call,” you’re probably missing something along the way!

When you’re selecting an answer choice that describes the graph, it’s important that the entire answer choice be true. For example, consider the answer choice that reads “For every level of education, as education increases the unemployment rate decreases.” For almost every level of education, as the level of education increases the unemployment rate decreases. So, choice B is almost true. But that last level – doctoral degree – has an unemployment rate just higher than the level before it (professional degree), so “every level” isn’t quite true. Make sure you read each choice critically and are careful with words that are hard to prove (every, all, always, never, none, etc.). “As the level of education increases, the unemployment rate and the median weekly income are positively correlated” is incorrect, again for just one word: the unemployment rate and the median weekly income are indeed correlated, but as income goes up the unemployment rate goes down. This is a negative – not positive – correlation.

“The median holder of an associate’s degree earns more than twice as much per week as the median person who has not completed high school” is also incorrect. The Associate’s Degree median is $768 while the median for no high school degree is $451. Since $768 is not quite twice as much as $451, this answer can be eliminated.

However, the first level of college degree listed is an Associate’s Degree, with an unemployment rate of 6.8%, and all other degrees listed have unemployment rates less than that. Since the unemployment rate for those without high school degrees is 14.1%, you can conclude that this rate is more than double the rate for any college degree, meaning that any college degree will have a rate of less than half the rate for no high school degree. This makes “The average holder of any type of college degree is less than half as likely to be unemployed as is the average person who has not completed high school” our correct answer.

Very often with line graphs, the SAT will ask you to describe a trend evident from the graph. In these cases, it’s helpful to get a quick glance at the graph to notice extremes (Where is the line the highest? Where is it the lowest? Are there any places where it stays flat for multiple increments?), but ultimately you’ll need to utilize Process of Elimination with the answer choices. We cannot conclude that “Average wind speed increases steadily between 5:00 am and midnight” because the graph clearly shows periods where the line goes down after 5:00 but before 24:00. Therefore the average wind speed does not increase steadily; in some instances, it decreases. We are also unable to conclude that “Average wind speed is lowest between 3:00 and 5:00.” Although the period between 3:00 and 5:00 marks one of the lower points on the graph, the line dips even lower below the 6.6 line at 18:00.

We also want to be sure to check the scale on graph problems! The entire y-axis for this graph only spans 6.5 to 7.2 meters per second, so although the line jumps up sharply it only represents a small percentage increase. Thus, we can eliminate “Average wind speed more than doubles from 18:00 to 22:00. This leaves us with “Average wind speed is highest between 20:00 and 22:00,” our correct answer. The highest point on the line is at 21:00, between the stated times of 20:00 and 22:00.

Notice that 3 of the 4 answer choices include the term “line of best fit” with regard to a prediction. With scatter plots, the line of best fit can serve as a tool to predict where new data points will fall. In this case, the line of best fit represents where one would expect the world record to be at any given point between 1900 and 2100. Remember that a faster time will be a lower number (running the 100 meters in 9 seconds is faster than running it in 10 seconds). So, “The world records set between 1980 and 1995 were all faster than what the line of best fit predicts” is incorrect, as the data points from 1980 to 1995 are above the line of best fit, so slower than what would have been predicted. Additionally, each data point represents a new world record – a point in time at which the world record was broken. So you can look at the horizontal space between each data point to see how long the duration was in between. And between approximately 1930 and just after 1950 there are no data points, so you can conclude that the world record was not broken for a period of approximately 20 years. Thus, “Since 1900, the world record has never gone more than 15 years without being lowered” is incorrect.

“The world record time in 2050, in seconds, is predicted by the line of best fit to be less than half what it was in 1910” is also incorrect, and brings up another point critical to your work with graphs: look at the scale! Even though the line of best fit is much, much lower at 2050 than it was in 1910, the total scale goes from 9.4 seconds at the bottom to 10.8 seconds at the top. So there’s no chance for one data point to be half of another: half of 10.8 (the top data point) would be 5.4, and the graph doesn’t go that low. It’s quite common for the lines or bars on a graph to appear to have a much greater difference in size than is actually true, so always check the scale when answering questions dealing with percent change. However, because the data points between 2000 and 2010 are all below the line of best fit, those times were all faster than would have been predicted. Thus, “The world records set between 2000 and 2010 were all faster than what the line of best fit predicts” is our correct answer.

Perhaps the easiest way to miss a graph-based question is to answer based only on the image without consideration of the words that accompany it. So make sure you always take note of what, specifically, the graph is displaying. Here it’s the percentages of trips taken, which is critical. It may seem convincing that “Over half of all users of public transportation are bus riders” at first (“more than half” certainly applies to “bus”), but the units matter! You can’t conclude that more than half of all users are bus riders, just that more than half of all trips taken were by bus. Suppose, for example, that people who take the bus take it twice per day, but people who use heavy rail only use it once per week. Each user of the bus would then take 10 trips for every one trip that a heavy rail user takes, and in that case, you’d need a lot more heavy rail users than bus users to have 35% of all trips be taken by heavy rail. “45% of all miles traveled on public transportation are traveled by rail of some kind” is also incorrect, because we’re once again facing a units problem. You don’t know about the percentage of miles traveled via each public transportation service; you only know about the percentage of trips taken. “More people travel via paratransit than via ferry” makes the same mistake: it draws a conclusion about the percentage of people when the information you have is about the percentage of trips taken. This leaves us with our correct answer: “Over 40% of all public transportation trips are taken by rail of some kind.” This option correctly makes an inference about the percentage of trips taken, and if you check the actual numbers you’ll see that the three categories of rail add up to 45% of all trips taken. Therefore, it is true that rail accounts for more than 40% of all trips taken.

Sometimes the SAT will ask you a question about what the graph suggests will happen in the future. Here, you won’t always be able to find the exact answer simply by looking at the graph, but will instead have to pay attention – as always – to trends in the graph and to precision in wording in the answer choices.

“Not sell any” is a very strong statement, particularly when the bottom of the graph shows $700 worth of ice cream and you have data points near 55 degrees that are well above that line. It’s not likely (even though it’s technically possible) that sales would fall off the graph entirely with just a slight move leftward on the x-axis (temperature axis), so “not sell any ice cream on a day for which the high temperature is below 55 degrees” is incorrect.

Similarly, over $2,100 in sales would jump above the highest gridline on the graph, and the trend shows that the two closest data points to 90 degrees retreat slightly toward lower sales. Such a jump to over $2,100 is possible, but not entirely likely. Thus, we can eliminate “sell over $2,100 in ice cream on a day for which the high temperature is over 90 degrees.” The answer choice, “typically sell more ice cream on weekends than on weekdays” uses softer wording, but is problematic in its contents. The graph only shows information regarding temperature and sales, not about the day of week and sales, so even though this might very well be true, the graph gives no evidence to make this prediction.

“Usually sell less ice cream on days with lower temperatures than on days with higher temperatures” uses softer language than the previous two choices, something you should notice given that precision in wording matters quite a bit on graph problems. “Usually” is a bit easier to prove than “will,” and the general trend in the data supports this – the trend in the data points is from lower left (lower temperature, less sales revenue) to upper right (higher temperature, more sales revenue), so we’ve found our correct answer.

If we look at the first table, we can see that from 1990 to 2015 the world population did grow, which does support part of Malthus’s prediction. However, if we look at the second table, we see that from 1990-2015 the percentage of people living poverty actually decreases across each world region (and dramatically so in those regions that were >50% in 1990). Thus, as population increased, poverty decreased. This contradicts Mathus’s prediction overall so we can eliminate answer choices that claim to support his prediction: “ it supports Malthus’s prediction, because it shows that poverty is still a major problem in the world “ and “it supports Malthus’s prediction, because it demonstrates that poverty is a problem that can be solved in certain regions”.

Looking at the remaining options, “it contradicts Malthus’s prediction, because it demonstrates that poverty remains highest in the same regions of the world year after year” is a true statement based on the second table; however, this has nothing to do with Mathus’s prediction so we can eliminate it. This leaves us with, “it contradicts Malthus’s prediction, because it shows that poverty is decreasing even while the population is increasing” as the correct answer. This statement is supported by both of the tables and does contradict Malthus’s overall prediction because that tables show that as population increased, poverty decreased.

To answer this question, we need to compare the answer options to the two tables. When you are looking at the answer options, keep in mind that the correct answer must be supported by both tables, not just one. Let’s start with “in 1999, there were more people living in extreme poverty in South Asia than in East Asia and the Pacific”. Note that the table that compares regions only deals with percents (percentage of people in that region living in poverty) but not with actual numbers of people. Without an idea of how many people live in each region, we can’t compare total numbers. Next, “fewer people in Latin America & the Caribbean lived in poverty in 2008 than in 2002” has the same problem - without knowing how many people are in each region, we can’t draw conclusions about the total number of people (for example, if one region has one billion people and another has one hundred, you could take the same percentage of each region and get wildly different actual numbers). Answer choice “extreme poverty is not a major concern in Europe & Central Asia” is interesting in that it offers a value judgment - from the numbers you might think “only 1% of people in this region live in extreme poverty, and 1% isn’t a big number” but ask yourself: if it’s 1% of 500 million people, isn’t it possibly a major concern to those 5 million people? Value judgments like this are very hard to prove, and when you’re asked to draw a conclusion on the SAT you need to be able to prove your answer. This leaves us with, “as of 2015, less than 3.5 billion people in the world lived in extreme poverty”. Without even having to go back and reference the tables you should notice that this choice mentions a population size- which is discussed in the first table- and poverty level- which is covered in the second table. To double check, we can look at the first table and see that is 2015 there are 7.3 billion people in the world- which makes 3.5 billion people about half of the population. Looking at the second table in 2015 we can see that all poverty rates are substantially below 50%, so we can draw this conclusion.

When looking to draw conclusions from the data presented in a table, we’re looking for the conclusion that must be true based on the given information. Here, the percent change did not increase in each of the years - or, according to the table, in each 5 year period. So, this is not something we can conclude. We also don’t know that the annual rate of growth was greater in 2000 than in 1995. The annualized rate of growth given was higher in 1995 (.31) as compared to 2000 (.21). If we look to do the math, or even just broadly compare the change, we can see that the growth amount was higher for the female population between 1947 and 2000 than it was for the male population. We do, however, know that “The total population of Japan exceeded 100,000 for each of the years displayed in the table.” This may not seem immediately obvious - but keep in mind, the data is displayed in thousands! So, even the smallest total population (that of 1947) was 78,010,000 - well over 100,000!

In this question, we’re being asked to apply estimation and rounding to compare the percentage of its annual budget each city spent on sanitation. If we use a bit of estimation, we can round the percents, in fraction form, as follows:

Andersonville:

Bronxtown: (we can round a bit more generously to , or and recognize that even if we’re not precise, Bronxtown is certainly less than all other cities.

Chadwick:

Dodgeville:

Edgewater:

So, by the process of elimination, we can see that Edgewater did in fact spend the largest percentage of its annual budget on sanitation. All incorrect answers are also quickly able to be disproven using the estimated fractions above.

This table provides us with an abundance of information - far more than we could feasibly be asked about in any one question. So, process of elimination is our friend here. If we look to our correct answer, “Every orange scented product experienced growth in unit sales from 2009 to 2010,” we can see that in each row for “orange,” the “% change” in unit sales is positive. Thus, we’ve found our correct answer! We cannot, however, conclude that “The product with the highest unit sales also had the highest percent change in dollar sales.” This is a tricky one. Superclean Spray Fresh comes in at a 23.2% increase over the last year. If we scan the rest of the column for percent change in dollar sales, we can see that this is the highest percent *increase* but not the highest percent *change,* as Deluxe Powder Lemon experienced a 23.8% decrease during this period. We also cannot conclude that “The product with the highest unit sales also had the highest dollar sales.” If we again look to Superclean Spray Fresh and scan to see if its dollar sales are also the highest, we quickly see that they are surpassed by the next cleaner up, Ultrashine Powder Lemon. Finally, it is untrue that every lemon scented bathroom cleaner sold more units in 2009 than in 2010. If we scan for lemon cleaners, we can quickly see that several have a negative “% change” in unit sales.

This table provides us with an abundance of information - far more than we could feasibly be asked about in any one question. So, process of elimination is our friend here. The table is already sorted such that we can easily identify the products with the highest and lowest dollar sales. Here, we cannot conclude that “The product with the lowest dollar sales in 2010 also had the lowest average price,” since Incredible Spray Lemon, our lowest dollar sales for 2010 costs $2.90, but if we scan the column for price, we can see that Deluxe Aerosol Orange comes in at a lower average price of $2.61, as does Dirt Blaster Spray Orange at $2.80. We also cannot conclude that “No product experienced growth in dollar sales but a decline in unit sales from 2009 to 2010.” If we scan the portion of the table where “% change” in dollar sales is positive, we will still find cases where “% change” in units is negative (for instance, Mrs. Grime Spray Unscented). We can also disprove that “The product with the highest dollar sales in 2010 also had the highest average price,” Since Ultra Shine Powder Lemon rings in at $3.99, and several other products have average prices above $4.

We can, however, conclude that “Spray bathroom cleaners generated more dollar sales than any other single type of bathroom cleaner in 2010,” but we’ll need to do a bit of estimation, math, and comparison to get there. Our only job is to try to identify whether any other type could have outsold “spray” cleaners. Of our varieties, Powder cleaners are irrelevant - there are only two such cleaners and the leading cleaner doesn't have enough separation from the field to make it a runaway category. The decision to be made is between Spray and Aerosol, so your mission is to determine which sold more. You can effectively do this by looking to the gap between the two, rather than the total. Spray starts with two higher-sellers than Aerosol, earning approximately $33M and $27M to Aerosol's two biggest totals, $22M and $21M. This gives Spray a $17M "gap" that Aerosol needs to make up, and with the next highest seller also a Spray Cleaner, the gap widens to nearly $18M. From there, you can simply compare one-to-one the remaining Spray and Aerosol cleaners on the Dollar Sales list to see whether the gap will come down to something competitive. It does not - notice that further down the list the dollar figures become so small that they'll make little if any dent in that gap between Spray totals and Aerosol totals. Rather than calculate, you can logically call this one a runaway just by judging the gaps at the top of the list and noting the limited opportunities for Aerosol to close it down.

When we’re asked to draw a conclusion that “must be true” based on the passage and/or table, we’ll want to use the process of elimination as a primary tactic. Here, we cannot determine that either month-by-month or in total, the level/percent change continue to decrease as we move chronologically through the listed events in the table. While this is true for the most part, in each case, we have a situation where this decreasing trend does not hold true. Additionally, we have no way of connecting the percent change to the impact on the economy, particularly because we don’t know how much the product at hand impacts the economy, or how long the bubble was in place for.

We can, however, conclude that “Percent change may not be the only factor contributing toward the economic bubble status of an economic event,” since the passage points out that despite the impressive level of percent change, a usual indicator of an economic bubble, “tulip mania” may not have, itself, qualified as one.

In this example, we’re looking to understand which option the table provides direct support for. Since the table does not include any information about either the conclusive vs. inconclusive nature of the percent data or any other factors that might come into play, and instead simply expresses the percent data, we can eliminate any option that addresses the idea that the “tulip mania” may not have represented an economic bubble. Additionally, while it is true that, based on the passage, “This phenomenon was so well-known that it has come to be the way many refer to an economic bubble,” we don’t have any direct support for this statement in the table. That said, the fact that the percent change both month-over-month and overall was highest for “tulip mania” as compared to all other economic bubbles supports the idea that “The extent of the change in price certainly merits its status as an economic bubble.”

In this example, we need to be careful to address the type of data we’ve been presented with in the table. Here, we were given the percent of individuals in each region who report believing in the supernatural. So, without population data, we cannot draw any conclusions about the *number* of individuals in each group with this belief. (Remember not to bring any outside information into your analysis!) Thus, we can eliminate “The same number of people believed in ghosts in the Americas in 2000 as believed in ghosts in Africa during that time” and “More people believed in ghosts in Africa in 2010 than believed in them in Europe during that time.”

We also cannot conclude that “For each region, belief in ghosts grew between 2000 and 2010,” as there is a clear decrease in the percent of people who believe in ghosts in the region for both the Americas and Asia. We can, however, conclude that “Belief in ghosts was more prevalent in Asia than in any other region in 2010,” as a higher percentage of the population in Asia reported believing in the supernatural than did any other region in 2010. Keep in mind, even if you weren’t sure the meaning of the word “prevalent,” we can use context and process of elimination to arrive at the correct answer, as we have here.

In this example, we’re looking for an answer option that aligns with, and thus helps to explain, the data trends represented in the table. If “A widespread cultural trend toward television programs that hunt for and expose supernatural forces became popular in America during the period between 2000 and 2010,” we would expect this trend to increase belief in the supernatural - but such belief decreased in the Americas during this period, allowing us to eliminate this option. The fact that “Europe has long been known to have a population with a particular affinity for belief in ghosts as compared to the other major regions of the world,” since Europe had the lowest percentage who reported believing in the supernatural in both 2000 and in 2010. If “In America, belief in the supernatural and astrological belief, an increasing trend between 2000 and 2010, tend to be strongly positively correlated with one another,” we would again expect belief in the supernatural to have increased among Americans during this time. The data, however, shows us that this was not the case, so this option can also be eliminated.

This leaves us with our correct answer: “In Africa, an improvement in educational access in rural regions included a learning module explaining the science behind a phenomenon previously believed by many to be the work of the supernatural.” If access to education allowed for more widespread knowledge of the science behind a phenomenon previously believed to be the work of the supernatural, this could provide us with a rationale for why the percent of the population in Africa who reported believing in the supernatural decreased during this time.