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Statistics - Graphic Displays

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    Study Guide Statistics – Graphic Displays 1. Bar Chart A bar chart is one of the most common ways to show numerical data visually. It uses rectangular bars to represent different categories, making it easy to compare amounts at a glance. One way to pictorially display the numbers shown in Table 1 (from “What Are Graphic Displays for Statistics?” ) is by using a bar chart . Vertical Bar Chart Figure 1. Vertical bar chart presentation of the expenditures of a college undergraduate for the past year. In a vertical 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 the heights of the bars , you can quickly see how expenses differ: • Room and board costs are nearly twice as much as tuition fees. • Tuition fees are more than double the 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 Guide Horizontal Bar Chart Figure 2. Horizontal bar chart presentation of the expenditures of a college undergraduate for the past year. A bar chart can also be shown horizontally , with the bars extending from left to right instead of bottom 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. 1.1 Important Features of Bar Charts No matter whether the bar chart is vertical or horizontal, several key features remain the same: • The bars are usually arranged from highest to lowest or lowest to highest , which makes comparisons clearer. • Space is left between bars to show that each bar represents a separate category. • The baseline (the bottom line in Figure 1 and the left side in Figure 2) represents zero . This is common, though not always required. • Even though the lengths of the bars differ , their thickness is always the same . This ensures that comparisons are based only on value, not appearance.

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    Study Guide 1.2 Why Bar Charts Are Useful Bar charts allow students to: • Compare categories quickly • Spot large and small values easily • Understand data without complicated calculations Because of their clarity and simplicity, bar charts are one of the most widely used tools in descriptive statistics. 2. Quiz: Bar Chart 1. Question How many students have a cat? Answer Choices • 8 • 10 • 13 Correct Answer 10 Why This Is Correct By looking at the bar labeled “Cat” on the bar chart, its height reaches 10 on the frequency scale. This shows that 10 students reported having a cat as a pet. 2. Question How many students have a dog or a fish?

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    Study Guide Answer Choices • 8 • 13 • 21 Correct Answer 21 Why This Is Correct From the bar chart: • Dogs have a frequency of 13 • Fish have a frequency of 8 To find how many students have a dog or a fish, we add the two values: 13 + 8 = 21 3. Question Which type of pet has a frequency of 6? Answer Choices • bird • fish • other Correct Answer bird Why This Is Correct The bar for birds reaches 6 on the frequency scale. This means 6 students reported 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 Guide 3. Pie Charts Bar charts are useful, but they have one main limitation. It can be hard to quickly see what part of the total each item represents. When understanding parts of a whole is important, a pie chart is often a better choice. 3.1 Why Use a Pie Chart? A pie chart shows how a total amount is divided among different categories. Each category is represented by a slice of the circle. The size of each slice shows how large that category is compared to the entire total. Pie charts are especially helpful because: • They clearly show proportions of the whole • They often display percentages , making comparisons easier • They give a quick visual summary of the data Example: Undergraduate Expenditures Using data on a college undergraduate’s expenses for one year, we can create a pie chart like the one shown in Figure 1 . This chart shows how money is spent on categories such as tuition, room and board, 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 Guide 3.2 How to Read a Pie Chart • The entire circle represents 100% of the total expenses. • Each slice of the pie represents one category. • The larger the slice , the greater that category’s share of the total. • The slices are arranged from largest to smallest to make the chart easier to understand. For example, if tuition takes up the largest slice, it means tuition accounts for the biggest portion of the student’s total spending. 3.3 When Pie Charts Work Best Pie charts are most effective when: • There are only a few categories • The goal is to compare parts of a whole If 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 Guide 4. Quiz: Pie Chart 1. Question What percent of people preferred Brand E ? Answer Choices • 16% • 24% • 32% Correct Answer 24% Why This Is Correct From the pie chart, Brand E occupies nearly one - fourth of the total circle, which corresponds to 24% of the total preferences. 2. Question How many people preferred Brand C ? Answer Choices • 10 • 15 • 20 Correct Answer 15 Why This Is Correct

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    Study Guide The pie chart shows Brand C representing 15% of the total. If the total number of people surveyed is 100, then 15% = 15 people . 3. Question Which brand is preferred by 16 people ? Answer Choices • A • B • C Correct Answer Brand A Why This Is Correct Brand A accounts for 16% of the total preferences. Since the total number of people is 100, 16% equals 16 people , matching Brand A. 4. Question What percent of people preferred Brand A or Brand D ? Answer Choices • 16% • 32% • 48% Correct Answer 32%

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    Study Guide Why This Is Correct Brand A represents 16% and Brand D represents 16% . Adding them together: 16% + 16% = 32% 5. Question Which brand is preferred by 8% of the people? Answer Choices • A • B • C Correct Answer Brand B Why This Is Correct The smallest section of the pie chart corresponds to 8% , which is labeled as Brand B . 5. Dot Plots A dot plot is a simple graph used to display quantitative data , which means data made up of numerical values. Dot plots are especially useful when working with a small set of numbers . 5.1 What Is a Dot Plot? In a dot plot: • Each dot represents one data value • The dots are placed along a number line • If more than one value is the same, the dots are stacked above that number This makes it easy to see where values are concentrated and how they are spread out.

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    Study Guide Example: Undergraduate Expenses Using the same undergraduate expense data from earlier, suppose we are only interested in comparing the dollar amounts spent. We are not concerned about what category each expense belongs 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 represent expenditure cost in thousands of dollars . Each dot shows one expense amount. When several dots appear above the same value, it means that amount occurred more than once. 5.2 Why 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 values However, dot plots work best with small data sets . If there are too many values, the graph can become crowded and harder to read.

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