You could immediately see that hypertension is more prevalent in older age groups. You could also say that at the prevalence of hypertension in the 45–54 age group (more than 40%) exceeds the average preva- lence among all age groups (30%). This graph could have been packed with more information. It could have included the hypertension prevalence among men and women. In that case, there would be three bars for each age group, and each bar would be labeled (for men, women, and both sexes) by using a different shading pat- tern, for example. Some bar graphs have horizontal bars, rather than vertical bars. Don’t be alarmed if you see them on the ACT. You could analyze them using the same skills you would for analyzing a bar graph with vertical bars. PIE GRAPHS Pie graphs are often used to show what percent of a total is taken up by different components of that whole. The pie chart below illustrates the relative productivity (new plant material produced in one year) of differ- ent biomes (desert, tundra, etc.). Relative Productivity of Biomes Desert 1% Tundra 2% Chaparral 11% Grassland 9% Taiga 12% Savanna 14% Temperate deciduous forest 18% Tropical rain forest 33% Hypertension among Different Age Groups 50 70 60 40 30 20 10 0 all ages 18–24 25–34 35–44 45–54 55–64 65–74 Prevalence of hypertension (%) Age group – ACT SCIENCE REASONING TEST PRACTICE– 264 If this chart appeared on the ACT, you could be asked for the percent of total world productivity of a specific biome. For example, savannas make up 14% of the total productivity. Or you may be asked which biome is the most productive (tropical rain forest) and which one is the least productive (desert). You could also be asked to compare the productivity of two different biomes. For example, you could state that tem- perate deciduous forest productivity (18%) exceeds the taiga productivity (12%). A test passage may also present you with two different, but related, pie charts and ask you to compare them. For example, humans can have one of four different blood types (A, B, AB, and O). The percent of peo- ple with a particular blood group is different in different geographic (gene pool) areas. You could be asked to compare a pie chart illustrating the blood group distribution in Europe with another pie chart illustrat- ing the blood group distribution in Asia. Diagrams Diagrams could be used to show a sequence of events, a process, the setup of a science experiment, a phe- nomenon, or the relationship between different events or beings. Here are some examples that you might find in your science textbooks: ■ diagram of the phases of cell division (Biology)—sequence of events ■ diagrams showing the oxygen and nitrogen cycle (Earth and Space Science)—process ■ diagram illustrating the titration technique (Chemistry)—setup of an experiment ■ diagram showing the focusing of a lens (Physics)—phenomenon ■ pedigree diagram for color-blindness (Biology)—relationship between events When you see a diagram, first ask yourself what the purpose of it is. What is it trying to illustrate? Then look at the different labeled parts of the diagram. What is their function? How are they interrelated? Take a look at the diagram below: Energy less stable product Initial state more stable product ∆ Ea ∆ Ea = energy barrier to forming more stable product ∆ Eb = energy barrier to forming less stable product ∆ Eb – ACT SCIENCE REASONING TEST PRACTICE– 265 In this diagram, we can see an initial state, connected to two different products. Immediately, we can say that two different products can form from the initial state. And, according to the label, the product rep- resented by the diamond is less stable than the product represented by the cup shaped figure. We also notice that the top portion of the curve connecting the initial states to the products is an energy barrier (explained in the legend in the lower right corner of the diagram). All the way on the left of the diagram, there is an arrow, pointing up and labeled “Energy.” Putting all this information together, we should be able to state the fol- lowing: ■ The diagram shows the energy of an initial state and the two products that can result from it. ■ The energy of the less stable product is higher than the energy of the more stable product. ■ The energy of the initial state is higher than the energy of either product. ■ The energy barrier for the formation of the less stable product is lower than the energy barrier for the formation of the more stable product. The Main Idea To quickly answer ACT questions on data representation, it’s important to get the big picture, or main idea of the graph, table, or diagram before you get bogged down in the details. The best way to do this is to first look at the title of the graphic you are presented with, if there is one. This will give you a summary of what the graphic is showing. The names of some of the graphics used in preceding examples were left out. Can you come up with appropriate titles for those graphics? After looking at the title, look at the axes, if there are any. What are the variables? Then look at legends and labels if they are included. Only when you understand what the graph is portraying and how the information is organize should you look for specific, detailed informa- tion. In the long run, this strategy will save you time and provide you with a sense of purpose and direction. Types of Data Representation Questions Most data representation questions on the ACT fall into one of these categories: ■ Interpretation (reading a table, graph, or diagram) ■ Comparison (making a statement about two or more different data points) ■ Making predictions (interpolation and extrapolation) ■ Drawing conclusions (using data to make a general statement) We will discuss each question type separately in the paragraphs and examples that follow. INTERPRETATION Questions about one specific piece of information presented in a graphic are usually interpretation questions. Questions of this type tend to be easier, and involve only reading the graphic correctly. Examples (using graphics already reviewed in this chapter) include: – ACT SCIENCE REASONING TEST PRACTICE– 266 1. What time does the train that leaves Congers Station at 12:19 P.M. arrive to Nyack? 2. What is the thermal conductivity of iron at 400 K? 3. What is the index of refraction of water at 400 nm? 4. What is the concentration of LH on the day 15 of the menstrual cycle? 5. In which age groups is the prevalence of hypertension less than 20%? 6. What is the relative productivity of grasslands? Answer these questions for practice and then look at the answers below to check how you’ve done. Answers 1. 12:46 P.M. 2. 69 W/m K 3. about 1.34 4. 30 units/ml 5. 18–24 and 25–34 6. 9% C OMPARISON Comparison questions involve making a statement about the relative magnitude or relative change in mag- nitude of two or more data points, or about the trends in different sets of data. The best strategy for answer- ing this type of question is to first find the data you are asked about, and then to compare them. Here are sample questions, based on graphics used as examples in previous sections. 1. Does it take more time to get from Congers Station to New City, or from New City to Valley Cottage? 2. Which metal has the lowest thermal conductivity at 100 K? 3. Is the concentration of progesterone greater in the first or the second half of the menstrual cycle? 4. Which biome has a productivity that is closest to the productivity of taiga? – ACT SCIENCE REASONING TEST PRACTICE– 267 Answers 1. Congers Station to New City takes more time 2. Platinum 3. It’s greater in the second half 4. Chaparral MAKING PREDICTIONS ACT questions that require you to make a prediction tend to be the most difficult, since they require true understanding. However, if you learn to interpolate and extrapolate, you will improve your ability to answer even the most difficult questions. To interpolate means to estimate the value of y for a value of x (or vice versa) between tabulated or graphed points. An example of interpolation would be estimating the thermal conductivity of copper at 250 K. What you would need to do is to is locate the adjacent temperature data points (200 K and 300 K) and read the thermal conductivity at those temperatures. That would give you a range in which the thermal conduc- tivity at 250 has to fall in. If the change of thermal conductivity with temperature were linear (constant slope, i.e. constant change with a fixed increment in temperature), it would be sufficient to get an average of the ther- mal conductivities at the adjacent temperatures. But if two choices on the ACT were both in the acceptable range of thermal conductivities, you would probably need to make a rough scatter plot of a few data points (with the temperature on the x-axis, and the thermal conductivity on the y-axis). Connect the points with a line or curve, and then determine whether the conductivity at 250 K is closer to the conductivity at 200 K, or to the conductivity at 300 K. That should help you reduce your choices to the correct answer. Here is the quick scatter plot just described. As you can see, the thermal conductivity of copper at 250 K is 400 W/m K, much closer to the thermal conductivity at 300 K, than to the thermal conductivity at 200 K. To extrapolate means to estimate the value of a variable beyond the range of the data provided. When you extrapolate, you assume that a trend you have observed extends all directions (future, past, increasing temperature, decreasing temperature, etc.). Most commonly (and conveniently) data extrapolation is Thermal Conductivity of Copper as a Function of Temperature 450 550 500 400 350 300 250 200 150 100 50 0 0 100 200 300 400 500 600 Thermal conductivity [W/mK] Temperature [K] – ACT SCIENCE REASONING TEST PRACTICE– 268 performed on scatter plots. Here is an example. The scatter plot shows the concentration of a reactant (con- sumed in a chemical reaction) as a function of time. Notice that data were not taken at the beginning of the experiment (zero seconds) and beyond 500 sec- onds. If you assume that the thick line will maintain its shape in both directions, you can solve this problem. At the beginning of the experiment the concentration of the reactant was at a maximum. Therefore, it had to be higher than 0.15 mol/liter. If you extend the thick data line to the y-axis (the gridline corresponding to zero seconds), while maintaining the shape of the curve, you can estimate the initial concentration of the reac- tant was about 0.18 mol/liter. How about the concentration at 600 seconds? At 300 seconds, the concentra- tion of the reactant seems to have leveled of at 0.05 mol/liter. It stays the same at 400 seconds, at 450 seconds, and 500 seconds. Wouldn’t you bet that the concentration will remain 0.05 mol/l at 600 seconds? DRAWING CONCLUSIONS To draw a conclusion, we take all available facts into account, and make a decision or statement based on all these facts put together. Question: Did he do it? Facts: The accused had a motive, no alibi, and the unfortunate luck of being seen by the nosy neighbor. Conclusion: The accused is guilty. In the case of science, in very much the same way, we need to pull all the information available together, sum it up, and make a judgment or prediction. Example 1 Question: If you were looking for a metal whose heat transfer properties didn’t vary much over a wide range of temperature, which metal from the list in the preceding example would you use? Concentration of a Reactant as a Function of Time 0.20 0.15 0.10 0.05 0.00 0 100 200 300 400 500 600 Concentration [mol/liter] Time [s] – ACT SCIENCE REASONING TEST PRACTICE– 269 . Different Age Groups 50 70 60 40 30 20 10 0 all ages 18–24 25–34 35–44 45–54 55 64 65 –74 Prevalence of hypertension (%) Age group – ACT SCIENCE REASONING TEST PRACTICE– 264 If this chart appeared. easier, and involve only reading the graphic correctly. Examples (using graphics already reviewed in this chapter) include: – ACT SCIENCE REASONING TEST PRACTICE– 266 1. What time does the train. than 20%? 6. What is the relative productivity of grasslands? Answer these questions for practice and then look at the answers below to check how you’ve done. Answers 1. 12: 46 P.M. 2. 69 W/m K 3.