Statistical Tables and Graphs Unit 5C Statistical Tables and Graphs Ms. Young

Frequency Tables A basic frequency table has two columns: The first column lists the categories of data. The second column lists the frequency of each category, which is the number of times each category appears in the data set. Additional columns may include relative frequency (frequency expressed as a fraction or percentage of the total) or cumulative frequency (total of frequencies for the given category and all previous categories). Ms. Young

Data Types and Binning Qualitative data describe qualities or categories. Quantitative data represent counts or measurements. When dealing with quantitative data categories, it is often useful to group, or bin, the data into categories that cover a range of possible values. Ms. Young

Summarizing Raw Data Consider the following 20 scores from a 100-point exam: 80 78 76 94 75 98 77 84 88 81 72 91 72 74 86 79 88 72 75 Determine appropriate bins and make a frequency table including columns for relative and cumulative frequency. Show students how to take raw data and do the following: 1) group data, 2) compute actual and relative frequencies, and 3) make a bar and a pie graph. Ms. Young

Bar and Pie Graphs A bar chart shows each category with a bar whose length corresponds to its frequency or relative frequency. Pie charts are used primarily for relative frequencies, because the total pie must always represent the total relative frequency of 100%. The size of each wedge is proportional to the relative frequency of the category it represents. Both graphs represent the same data set. Discuss the pros and cons of the graphs. Ms. Young

Bar and Pie Graphs The bar chart and pie chart below both show the data from table 5.1. Grade Data Both graphs represent the same data set. Discuss the pros and cons of the graphs. Grade Data Ms. Young

Important Labels for Graphs Title/caption: The graph should have a title or caption (or both) that explains what is being shown and, if applicable, lists the source of the data. Vertical scale and title: Numbers along the vertical axis should clearly indicate the scale. The numbers should line up with the tick marks. Include a label that describes the variable. Horizontal scale and title: The categories should be clearly indicated along the horizontal axis. (Tick marks may not be necessary for qualitative data, but should be included for quantitative data.) Include a label that describes the variable. Legend: If multiple data sets are displayed on a single graph, include a legend or key to identify the individual data sets. Ms. Young

Definitions A histogram is a bar graph for quantitative data categories. The bars have a natural order and the bar widths have specific meaning. A line chart shows the data value for each category as a dot, and the dots are connected with lines. For each dot, the horizontal position is the center of the bin it represents and the vertical position is the data value for the bin. A time-series diagram is a histogram or line chart in which the horizontal axis represents time. Ms. Young

Histogram and Line Chart The histogram and line chart below both show the same data. Both graphs represent the same data set. Discuss the pros and cons of the graphs. Ms. Young

Reading Time-Series Diagrams A time-series line chart of stock, bond, and gold prices for an initial $100 investment is shown below. If you invested $100 in bonds on July 7, how much would your investment be worth on August 25? About $97.50 Ms. Young