Displaying Data: Dot Plots Stem and Leaf Plots Grouped Frequency Tables Histograms and Bar Graphs

Graphs are used to try to tell a story.

Dot Plots A dot plot, or line plot, provides a quick and simple way of organizing numerical data. They are typically used when there is only one group of data with fewer than 50 values.

Dot Plots Suppose the 30 students in Abel’s class received the following test scores:

Dot Plots A dot plot for the class scores consists of a horizontal number line on which each score is denoted by a dot, or an x, above the corresponding number-line value. The number of x’s above each score indicates how many times each score occurred.

Dot plots Four students scored 82. A gap occurs between scores 88 and 97. Two students scored 72. The score 52 is an outlier Scores 97 and 98 form a cluster

Dot Plots Outlier a data point whose value is significantly greater than or less than other values Cluster an isolated group of points Gap a large space between data points Mode data value(s) that occur most often.

Stem and Leaf Plots How to construct a stem-and-leaf plot: Find the high and low values of the data. Decide on the stems. List the stems in a column from least to greatest. Use each piece of data to create leaves to the right of the stems on the appropriate rows.

Stem and Leaf Plots List the leaves in order from least to greatest. Add a legend identifying the values represented by the stems and leaves. Add a title explaining what the graph is about.

Stem and Leaf Plots The stem and leaf plot is similar to the dot plot, but the number line is usually vertical, and digits are used rather than x’s. 9 | 7 represents 97.

Create a stem-and-leaf plot Cost of First year tuition at universities in the UNC system (in thousands of dollars) 3.4, 5.3, 4.0, 4.1, 3.5, 2.8, 5.1, 3.3, 3.6, 4.0, 4.4, 4.0. 4.2, 4.3, 4.0 In your notes create a stem-and-leaf plot based on this information. Be sure to label the plot.

Frequency Tables Group the presidents into two groups, George Washington to Rutherford B. Hayes and James Garfield to Ronald Reagan.

Frequency Tables A grouped frequency table shows how many times data occurs in a range. The data for the ages of the presidents at death are summarized in the table.

Frequency Tables Characteristics of Frequency Tables Each interval has the same size. We know how many data values occur within a particular interval but we do not know the particular data values themselves.

Frequency Tables Characteristics of Frequency Tables As the interval size increases, information is lost. Classes (intervals) should not overlap.

Histograms and Bar Graphs A histogram is made up of adjoining rectangles, or bars. The bars are all the same width. The scale on the vertical axis must be uniform.

Histograms and Bar Graphs The death ages are shown on the horizontal axis and the numbers along the vertical axis give the scale for the frequency. Frequencies are shown by the heights of vertical bars each having same width. Uniform scale

Bar Graphs A bar graph typically has spaces between the bars and is used to depict categorical data. The bars representing Tom, Dick, Mary, Joy, and Jane could be placed in any order.

Histograms and Bar Graphs A distinguishing feature between histograms and bar graphs is that there is no ordering that has to be done among the bars of the bar graph, whereas there is an order for a histogram.

Double-Bar Graphs A double bar graph can be used to make comparisons in data.