UC MATH 1A - Chapter 6 Charts and Graphs

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Chapter 6 Charts and Graphs THE JOY OF VISUAL DATA GRE chart questions are pretty straightforward you read a couple of charts and or graphs and then you answer some questions about them Chart questions appear on a split screen the chart s appear on the left and the questions are on the right When a chart question pops up be sure to start by hitting the scroll bar to see just how much data you re dealing with There might be a second chart hidden below the first one so don t get thrown off if you see questions about a chart you don t think exists Chart questions test four primary skills how well you read charts how well you approximate percentage and percentage change how well you calculate exact percentage and percentage change how well you synthesize related data from two separate sources When you have to answer chart questions there are a couple things to remember 1 Read all the charts Before you answer any questions about a set of charts look over the charts Make sure you pay particular attention to the units involved Is each axis in terms of a number of people a percentage a dollar amount Look for a legend for the charts Are we talking about 100 people or 100 million people Check to see if you need to scroll down for any additional charts If there are multiple charts spend a minute or so figuring out how the charts relate to each other Do the charts show different aspects of the same information For instance does one chart show the jobs of a group of people whereas the other chart shows the education level of those same people Does one chart give more detail about a limited sliver of information from the previous chart Spending time understanding the charts now will pay off later 2 Find the information you need Once you read a Charts question figure out which chart and which data points you need to look at 3 Use your scratch paper and label your information Find the data points you need to answer the question and write each one down on your scratch paper Include units and a name for each data point Don t just write 23 Write 2004 imports 23 mil tons It adds only an extra couple of seconds of time and makes it much less likely that you will make a mistake or get lost in the problem 4 Estimate before you calculate Look to eliminate answers before doing too many calculations If 226 of the 603 employees were fired and the question wants to know what percentage were fired then do a quick estimation 33 Since we rounded 226 down to 200 our answer will probably be a bit larger than 33 Cross off any answers that are 33 or less or much greater than 40 If we can t choose an exact answer based on our estimation then we can go back and calculate afterwards Percentage Change Quick Quiz Remember all the reading you did about percentages and percent change in Chapter 3 Well here are some questions Let s see how much skill you ve retained Explanations for Percentage Quick Quiz 1 If a stock portfolio grew from 1 200 to 1 600 then the change is 1 600 1 200 or 400 The percent change is or 100 or 33 The correct answer is B 2 If a portfolio with 1 600 in it has 30 of the money withdrawn then the amount of money withdrawn is 1 600 or 480 The portfolio has 1 600 480 or 1 120 remaining This can be solved in one fewer step by recognizing that withdrawing 30 is the same thing as leaving 70 70 of 1 600 is 1 120 The correct answer is E 3 The stock portfolio is worth 1 120 Quantity A is the value of the portfolio Quantity B states the portfolio increased by 25 then decreased by 25 If a stock portfolio worth 1 120 increase by 25 then the stock portfolio increases by 1120 or 280 to 1 400 Then if it lost 25 the value of the stock portfolio drops from 1 400 to or 1 050 Quantity A is greater than Quantity B so the correct answer is A 4 This problem states that a stock portfolio worth 1 600 increases by 200 Because 200 of 1 050 is 2 100 the new value of the portfolio is 1 050 2 100 or 3 150 5 A portfolio that began with 1 200 and ended with 3 150 increased in value by 3 150 1 200 1 950 To determine the percent increase divide 1 950 by 1 200 and multiply the result by 100 The portfolio grew 163 The correct answer is D FOCUS MINIMIZES CARELESSNESS Reading charts is a lot like interpreting points that are graphed on the coordinate plane It s a process that anyone can learn with practice The worst thing about GRE charts however is that they are often intentionally confusing and or difficult to read so it s easy to make careless mistakes under stressful conditions Above all else resolve to be calm and systematic when you navigate the data that the GRE throws at you If you can manage that the rest should fall into place nicely The Formats Most chart questions come in three formats bar or line graphs pie charts and data tables Additionally the test often gives you two separate charts that are somehow related however remotely Data tables are made up entirely of numbers so all you need to do is crunch the numbers Graphs and charts can be a little trickier because they require you to interpret them visually Bar Graphs On bar graphs data points are indicated with rectangular bars that can run either horizontally or vertically Bar graphs get tricky when one bar contains two or more bits of data that are often colored or patterned differently like this Line Graphs Line graphs are very similar to bar graphs except they link data points with lines that can indicate overall trends Pie Charts Pie charts divide up all data into wedges each of which indicates a percentage of the whole All of the percentages should total to 100 and the bigger the wedge the bigger the percentage Data Tables Sometimes the GRE does away with graphics altogether and simply presents raw data in several rows and columns Ballparking Redux Many times the numbers you ll work with will be approximations rather than exact calculations Working well with these approximations is an important skill Let s look at an example About how much bigger in terms of a percentage is the bar on the left than the bar on the right Pretty hard to tell isn t it Now look at those same bars placed next to each other When the bars are adjacent it s a little easier to compare their relative size The bar on the left is about half again as big or 50 bigger You can confirm this when the two bars are next to a …


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