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Basic Math and Pre-Algebra - Graphs

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    Study Guide Basic Math and Pre - Algebra – Graphs 1. Bar Graphs 1.1 What Is a Bar Graph? A bar graph shows information using rectangular bars. Each bar represents a category (like a city, year, or company). The length or height of the bar shows the amount. Usually: • One side lists the categories (cities, companies, years). • The other side shows numbers (like totals or amounts). When reading a bar graph, always ask: • What does each bar represent? • What units are being used? • What relationship is the question asking about? Example 1: Comparing Cities The bar graph shows the number of billboards in each city . The scale increases in increments of 100. From the graph: • City W ≈ 500 billboards • City Y ≈ 150 billboards To find how many more billboards City W has than City Y: So, City W has about 350 more billboards than City Y . Always estimate carefully using the scale shown.

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    Study Guide Figure 1 Example 2: Books Sold by Publishers Figure 2

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    Study Guide This bar graph shows the number of books sold (in millions) for three publishers from 1990 to 1992: • Mystery Mystery • Reference Unlimited • All Sports Each bar represents one year. Since the values are already in millions , you do not need to add extra zeros. Question 1 How many more books did Mystery Mystery sell than All Sports (total for 1990 – 1992)? Mystery Mystery Sales (in millions): • 1990: 2.5 • 1991: 2.5 • 1992: 3.4 Total: All Sports Sales (in millions): • 1990: 1 • 1991: 2.1 • 1992: 3 Total: Now subtract: So, Mystery Mystery sold 2.3 million more books than All Sports over those three years.

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    Study Guide Question 2 Which publisher had the greater percent increase from 1991 to 1992? To find percent increase, use this formula: Mystery Mystery 1991: 2.5 1992: 3.4 Change: Percent increase: All Sports 1991: 2.1 1992: 3 Change: Percent increase:

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    Study Guide Now compare: So, All Sports’ percent increase exceeded Mystery Mystery’s by about 7% . Question 3 What caused the 1992 decline in Reference Unlimited's book sales? This cannot be answered from the graph. The graph only shows numbers sold — it does not explain why sales changed. Important rule: Never assume information that is not shown in the graph. Helpful Tips for Reading Bar Graphs • Check the scale carefully. • Estimate only to the level of precision shown. • Do not assume extra information. • Use formulas when percent change is required. • Remember that “in millions” means the numbers are already large — no extra zeros needed. Summary Bar graphs organize data into visual bars, making comparisons easier. From this lesson, you learned: • How to compare totals using subtraction. • How to calculate percent increase using • How to avoid assuming information not shown. • How to carefully read scales and units.

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    Study Guide 2. Quiz: Bar Graphs 1. Question The maximum number of traffic lights for any city exceeded the minimum number of traffic signals by how many? Answer Choices • 4 • 5 • 8 Correct Answer ࿨ ࿩ ࿪ 8 Why This Is Correct From the graph, identify the city with the greatest number of traffic signals and the city with the fewest. Subtract the smallest value from the largest value. The difference between these two values is 8 . 2. Question Which city had 25% more traffic signals than City C? Answer Choices • City A • City B • City D

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    Study Guide Correct Answer ࿨ ࿩ ࿪ City D Why This Is Correct To find 25% more than City C, multiply City C’s value by 1.25. The city whose number matches that result is City D . 3. Question In which city is traffic congestion the worst? Answer Choices • City B • City D • cannot answer based on the graph Correct Answer ࿨ ࿩ ࿪ cannot answer based on the graph Why This Is Correct The graph only shows the number of traffic signals , not the amount of traffic congestion. More traffic lights does not necessarily mean worse congestion. So, this question cannot be answered from the graph alone . 4. Question If City B decreased the number of traffic signals by 1/4, it would have the same number of traffic signals as which city?

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    Study Guide Answer Choices • A • C • D Correct Answer ࿨ ࿩ ࿪ C Why This Is Correct Decreasing City B’s number by 1/4 means multiplying by 3/4 (or 0.75). After calculating, the new value matches the number of traffic signals in City C . 5. Question How does the average number of traffic signals for cities B, C, and D compare with the number of traffic signals in City A? Answer Choices • They are the same number. • The average number of traffic signals for cities B, C, and D exceeds the number of traffic signals in city A by 1. • The average number of traffic signals for city A exceeds the number of traffic signals in cities B, C, and D by 1. Correct Answer ࿨ ࿩ ࿪ The average number of traffic signals for cities B, C, and D exceeds the number of traffic signals in city A by 1. Why This Is Correct Add the numbers for cities B, C, and D. Divide by 3 to find the average. Comparing that average with City A shows it is 1 greater .

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    Study Guide 6. Question In 2010, the number of degrees in Science exceeded the number of degrees in Math by how many? Answer Choices • 3 • 30 • 300 Correct Answer ࿨ ࿩ ࿪ 30 Why This Is Correct Look at the 2010 values for Science and Math. Subtract the Math value from the Science value. The difference is 30 degrees . 7. Question Which of the following is true about the number of degrees awarded from 2008 to 2009? Answer Choices • Science and Math increased in number • English and Math increased in number • Science and English increased in number Correct Answer ࿨ ࿩ ࿪ Science and English increased in number Why This Is Correct Comparing the 2008 and 2009 bars on the graph shows that Science and English increased, while Math did not increase during that period.

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    Study Guide 8. Question Which of the following had the greatest percent change? Answer Choices • Other from 2008 to 2009 • Math from 2009 to 2010 • Science from 2009 to 2010 Correct Answer ࿨ ࿩ ࿪ Math from 2009 to 2010 Why This Is Correct Percent change is calculated by: (Change ÷ Original) × 100 Comparing the relative increases shows that Math from 2009 to 2010 had the greatest percentage increase. 9. Question By approximately what percent did the number of English degrees awarded change from 2009 to 2010? Answer Choices • 3% • 10% • 15% Correct Answer ࿨ ࿩ ࿪ 10%

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