EXPLORING QUANTITATIVE DATA

Analyzing One-Variable Data Lesson 1.3 Displaying Quantitative Data: Dotplots Statistics and Probability with Applications, 3rd Edition Starnes, Tabor Bedford Freeman Worth Publishers

Displaying Quantitative Data: Dotplots Learning Targets After this lesson, you should be able to: Make and interpret dotplots of quantitative data. Describe the shape of a distribution. Compare distributions of quantitative data with dotplots.

Think Before You Draw, Again Remember the “Make a picture” rule? Now that we are adding to our repertoire of data displays, you need to Think carefully about which type of display to make. Before making a stem-and-leaf display, a histogram, or a dotplot, check the Quantitative Data Condition: Be sure that the data are values of a quantitative variable whose units are known.

Displaying Quantitative Data: Dotplots You can use a bar chart or pie chart to display categorical data. A dotplot is the simplest graph for displaying quantitative data. Dotplot A dotplot shows each data value as a dot above its location on a number line.

Displaying Quantitative Data: Dotplots How to Make a Dotplot Draw and label the axis. Draw a horizontal axis and put the name of the quantitative variable underneath. Scale the axis. Look at the smallest and largest values in the data set. Start the horizontal axis at a number equal to or below the smallest value and place tick marks at equal intervals until you equal or exceed the largest value. Plot the values. Mark a dot above the location on the horizontal axis corresponding to each data value. Try to make all the dots the same size and space them out equally as you stack them.

Dotplots may also be displayed vertically: The dotplot to the right shows Kentucky Derby winning times, plotting each race as its own dot. You might see a dotplot displayed horizontally or vertically.

Displaying Quantitative Data: Dotplots When you describe the shape of a dotplot or other graph of quantitative data, focus on the main features. Look for major peaks, not for minor ups and downs in the graph. Look for clusters of values and obvious gaps. Look for rough symmetry or clear skewness. A distribution is roughly symmetric if the right and left sides of the graph are approximately mirror images of each other. A distribution is skewed to the right if the right side of the graph is much longer than the left side. It is skewed to the left if the left side of the graph is much longer than the right side. Roughly Symmetric Skewed-left Skewed-right

Displaying Quantitative Data Examining the Distribution of a Quantitative Variable The purpose of a graph is to help us understand the data. After you make a graph, always ask, “What do I see?”?” Displaying Quantitative Data How to Examine the Distribution of a Quantitative Variable In any graph, look for the overall pattern and for striking departures from that pattern. Describe the overall pattern of a distribution by its: Shape Center Spread Note individual values that fall outside the overall pattern. These departures are called outliers. Don’t forget your SOCS! 9

Displaying Quantitative Data: Dotplots How to Describe the Distribution of a Quantitative Variable You can describe the overall pattern of a distribution by its shape, center, and variability or spread. An important kind of departure is an outlier, a value that falls outside the overall pattern.

Displaying Quantitative Data: Dotplots When comparing distributions of quantitative data, it’s not enough just to list values for the center and spread of each distribution. You have to explicitly compare these values, using words like “greater than,” “less than,” or “about the same as.” How do the numbers of people living in households in the United Kingdom (U.K.) and South Africa compare?

How can we check the health of a stream? LESSON APP 1.3 How can we check the health of a stream? Nitrates are organic compounds that are a main ingredient in fertilizers. When those fertilizers run into streams, the nitrates can have a toxic effect on fish. An ecologist studying nitrate pollution in two streams measures nitrate concentrations at 42 places on Stony Brook and 42 places on Mill Brook. The parallel dotplots display the data. Explain what the dot above 12 in the Stony Brook graph represents. What percent of the nitrate concentration measurements for each stream exceeded 10 milligrams per liter (mg/l)? Compare the centers of these two distributions. Is the variability in nitrate concentrations for the two streams similar or different? Justify your answer.

Displaying Quantitative Data: Dotplots Learning Targets After this lesson, you should be able to: Make and interpret dotplots of quantitative data. Describe the shape of a distribution. Compare distributions of quantitative data with dotplots.