EXERCISE 4WORK OUT EACH PROBLEM. QUESTION 1 IS A GRID-IN QUESTION. FOR...

5. DATA ANALYSIS

The new SAT includes questions involving the analysis of data displayed in graphical formats such as tables, piegraphs, line charts, bar graphs, and scatter plots. To answer a data-analysis question, you’ll need to:* Understand how the data are displayed* Know which data are relevant to the question* Know how to process the relevant data to solve the problem (answer the question correctly)A data analysis question might require a simple arithmetic calculation (addition or subtraction) and/or a simplecalculation of a percent, average, fraction, or ratio.In handling SAT data analysis, be careful to read the question very carefully, so that you select the appropriategraphical data and perform the appropriate calculation — one that yields the answer to the precise question beingasked. In analyzing a line chart, bar graph, or scatter plot (see the examples below), estimating number values inthe display will suffice to answer the question correctly. To answer any data analysis question asking for anapproximation, rounding off your calculations will suffice.Example (Table):According to the table above, of the total number of automobiles sold to U.S. and foreigninstitutions during the 2002–03 model year, which of the following most closely approximates thepercent that were standard models?(A) 24%(B) 36%(C) 41%(D) 59%(E) 68%Solution:The correct answer is (D). The total number of units sold to institutions = (3.6 + 8.5 + 1.9) +(1.7 + 4.9 + 2.2) = 22.8. The number of these units that were standard models = (8.5 + 4.9) = 13.4.To answer the question, divide 13.4 by 22.8 (round off the quotient): 22.8 ÷ 13.4 ≈ .59, or 59%.Example (Pie Graph):Based on the data shown above, the combined area of Unit B and Unit D is approximately(A) 51,000 square feet(B) 57,500 square feet(C) 70,000 square feet(D) 74,500 square feet(E) 108,000 square feetThe correct answer is (D). The size of Unit B is 42% of 140,000 square feet, or about 59,000 squarefeet. Thus, the combined size of Unit B and Unit D is approximately 74,500 square feet.Example (Line Chart):Referring to the graph above, approximately what was the greatest dollar amount by which theshare price of ABC common stock exceeded the share price of XYZ common stock at the same timeduring year X?(A) $1.80(B) $2.60(C) $3.00(D) $3.60(E) It cannot be determined from the information given.The correct answer is (B). You’re looking for the point at which the dotted line (ABC’s stock price)is furthest above the solid line (XYZ’s stock price). The dotted line lies above the solid line onlyduring the second half of the 2nd quarter and the first half of the 3rd quarter; the end of the 2ndquarter marks the greatest difference between prices during that period. At that time, ABC stockwas priced at approximately $7.60, while XYZ stock was priced at approximately $5.00 per share.The difference between those two prices is $2.60.Example (Bar Graph):Referring to the data shown above, what is the approximate ratio of the average number of hoursper week that the youngest age group spent watching entertainment to the average number of hoursthat the other two groups combined spent watching entertainment?(A) 3:4(B) 1:1(C) 6:5(D) 5:3(E) 5:2The correct answer is (D). You’re task here is to compare the size of the entertainment portion ofthe left-hand bar to the combined sizes of the same portion of the other to bars. Size up the ratiovisually. The portion on the first chart is a bit larger than the other two combined, and so you’relooking for a ratio that’s greater than 1:1. Approximate the height of each three portions:13–18 age group: 25 hours19–24 age group: 5 hours25–30 age group: 10 hoursThe ratio in question is 25:15, or 5:3.Example (Scatter Plot):Companies A, B, C, D, and E all manufacturer and sell a similar product. The graph abovecompares manufacturing costs and sales prices per unit among the five companies. If all fivecompanies have sold the same number of units, which company has earned the greatest profit fromthose sales?(A) A(B) B(C) C(D) D(E) EThe correct answer is (E). Since the number of units sold was the same for all five companies, thegreatest profit was earned by the company with the highest price-to-cost ratio. You can compareratios by drawing a line segment from point 0 to each of the five plotted points. The segment withthe steepest slope (vertical change divided by horizontal change) indicates the greatest price-to-costratio. Segment

OE

has the steepest slope, and hence company E earned the greatest profit.