Statistics - Graphic Displays - Quick Guides

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Study GuideStatistics–Graphic Displays1.Bar ChartAbar chartis one of the most common ways to show numerical data visually. It uses rectangular barsto represent different categories, making it easy to compare amounts at a glance.One way to pictorially display the numbers shown inTable 1(from“What Are Graphic Displays forStatistics?”) is by using abar chart.Vertical Bar ChartFigure 1. Vertical bar chart presentation of the expenditures of a college undergraduate for thepast year.In avertical bar chart, the bars go up and down. Each bar represents a different expense category,such as room and board, tuition, transportation, or books and lab.By comparing theheights of the bars, you can quickly see how expenses differ:•Room and boardcosts are nearlytwice as muchas tuition fees.•Tuition feesare more thandoublethe expenses for books and lab and for transportation.This visual format makes it much easier to compare spending than looking at numbers in a table.

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Study GuideHorizontal Bar ChartFigure 2. Horizontal bar chart presentation of the expenditures of a college undergraduate forthe past year.A bar chart can also be shownhorizontally, with the bars extending from left to right instead ofbottom to top. The information displayed is the same—the layout is just different.Some people find horizontal bar charts easier to read, especially when category names are long.1.1Important Features of Bar ChartsNo matter whether the bar chart is vertical or horizontal, several key features remain the same:•The bars are usually arranged fromhighest to lowestorlowest to highest, which makescomparisons clearer.•Space is left between barsto show that each bar represents a separate category.•The baseline (the bottom line in Figure 1 and the left side in Figure 2) representszero. This iscommon, though not always required.•Even though thelengths of the bars differ, theirthickness is always the same. Thisensures that comparisons are based only on value, not appearance.

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Study Guide1.2Why Bar Charts Are UsefulBar charts allow students to:•Compare categories quickly•Spot large and small values easily•Understand data without complicated calculationsBecause of their clarity and simplicity, bar charts are one of the most widely used tools in descriptivestatistics.2.Quiz: Bar Chart1. QuestionHow many students have a cat?Answer Choices• 8• 10• 13Correct Answer10Why This Is CorrectBy looking at thebar labeled “Cat”on the bar chart, its height reaches10on the frequency scale.This shows that10 studentsreported having a cat as a pet.2. QuestionHow many students have a dog or a fish?

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Study GuideAnswer Choices• 8• 13• 21Correct Answer21Why This Is CorrectFrom the bar chart:•Dogshave a frequency of13•Fishhave a frequency of8To find how many students have a dogora fish, we add the two values:13 + 8 =213. QuestionWhich type of pet has a frequency of 6?Answer Choices• bird• fish• otherCorrect AnswerbirdWhy This Is CorrectThe bar forbirdsreaches6on the frequency scale.This means6 studentsreported having a bird as a pet.The bars for fish and other reach different values, so they are not correct.

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Study Guide3.Pie ChartsBar charts are useful, but they have one main limitation. It can be hard to quickly seewhat part ofthe totaleach item represents. When understandingparts of a wholeis important, apie chartisoften a better choice.3.1Why Use a Pie Chart?Apie chartshows how a total amount is divided among different categories. Each category isrepresented by a slice of the circle. The size of each slice shows how large that category is comparedto the entire total.Pie charts are especially helpful because:•They clearly showproportions of the whole•They often displaypercentages, making comparisons easier•They give a quick visual summary of the dataExample: Undergraduate ExpendituresUsing data on a college undergraduate’s expenses for one year, we can create a pie chart like theone shown inFigure 1. This chart shows how money is spent on categories such as tuition, room andboard, books, transportation, and other expenses.Figure 1.Pie chart presentation of the expenditures of a college undergraduate for the past year.

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Study Guide3.2How to Read a Pie Chart•Theentire circlerepresents 100% of the total expenses.•Eachslice of the pierepresents one category.•Thelarger the slice, the greater that category’s share of the total.•The slices are arranged fromlargest to smallestto make the chart easier to understand.For example, if tuition takes up the largest slice, it means tuition accounts for the biggest portion ofthe student’s total spending.3.3When Pie Charts Work BestPie charts are most effective when:•There areonly a few categories•The goal is to compareparts of a wholeIf there are too many categories, the chart can become crowded and confusing. In such cases,another type of graph may be more appropriate.

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Study Guide4.Quiz: Pie Chart1. QuestionWhat percent of people preferredBrand E?Answer Choices• 16%• 24%• 32%Correct Answer24%Why This Is CorrectFrom the pie chart, Brand E occupies nearly one-fourth of the total circle, which corresponds to24%of the total preferences.2. QuestionHow many people preferredBrand C?Answer Choices• 10• 15• 20Correct Answer15Why This Is Correct

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Study GuideThe pie chart shows Brand C representing15%of the total.If the total number of people surveyed is 100, then15% = 15 people.3. QuestionWhich brand is preferred by16 people?Answer Choices• A• B• CCorrect AnswerBrand AWhy This Is CorrectBrand A accounts for16%of the total preferences.Since the total number of people is 100,16% equals 16 people, matching Brand A.4. QuestionWhat percent of people preferredBrand A or Brand D?Answer Choices• 16%• 32%• 48%Correct Answer32%

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Study GuideWhy This Is CorrectBrand A represents16%and Brand D represents16%.Adding them together:16% + 16% = 32%5. QuestionWhich brand is preferred by8%of the people?Answer Choices• A• B• CCorrect AnswerBrand BWhy This Is CorrectThe smallest section of the pie chart corresponds to8%, which is labeled asBrand B.5.Dot PlotsAdot plotis a simple graph used to displayquantitative data, which means data made up ofnumerical values. Dot plots are especially useful when working with asmall set of numbers.5.1What Is a Dot Plot?In a dot plot:•Eachdot represents one data value•The dots are placed along anumber line•If more than one value is the same, the dots are stacked above that numberThis makes it easy to see where values are concentrated and how they are spread out.

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Study GuideExample: Undergraduate ExpensesUsing the same undergraduate expense data from earlier, suppose we are only interested incomparing thedollar amountsspent. We are not concerned about what category each expensebelongs to.In this case, a dot plot works well.Figure 1. Dot plot of the expenditures of a college undergraduate for the past year.On the horizontal axis, the numbers representexpenditure cost in thousands of dollars. Each dotshows one expense amount. When several dots appear above the same value, it means that amountoccurred more than once.5.2Why Use a Dot Plot?Dot plots are helpful because they:•Show individual data values clearly•Make it easy to compare amounts•Help identify clusters, gaps, or unusual valuesHowever, dot plots work best withsmall data sets. If there are too many values, the graph canbecome crowded and harder to read.

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