Notes 5C: Statistical Tables and Graphs Frequency Tables A frequency table is an easy way to display raw data. A frequency table typically has between two to four columns: The first column lists all the categories of data The second column lists the frequency or number of times each category appears The third column lists the relative frequency (frequency expressed as a fraction or % of total) The fourth column lists the cumulative frequency (total of frequencies for the given category and all previous categories) 1) Make a frequency table of the grades earned by 25 students on an essay exam. The grades are given below. A C C B C D C C F D C C C B B A B D B A A B F C B Grade Frequency Relative Frequency Cumulative Frequency A B C D F Total What are the categories? What is the relative frequency for a B? (What % of the students received a B?) What is the cumulative frequency of a C? (How many students made a C or better?) 2) Does the following statement make sense? (explain). I made a frequency table with two columns, one labeled State and one labeled State Capitol.
Data Types The data in the categories fall into two types, qualitative and quantitative. Qualitative data describe qualities, attributes, opinions, or observations that are not measured. Quantitative data represent actual measurements or counts. In problem #1, the grades A, B, C, D, F are qualitative because they represent qualities such as excellent, average, or bad. In contrast, scores like 38/50 or 76% are quantitative because they represent an actual measurement. 3) Classify each of the following types of data as either qualitative or quantitative. a) Brand names of shoes in a consumer survey b) Heights of students c) Audience ratings of a film on a scale of 1 to 5, where 5 means excellent Binning Data When there is a wide range of quantitative values, it s often useful to group, or bin the data into categories that cover a span of possible values. For example, in a table of income levels, it might be useful to create bins of $1 to $20,000, $20,001 to $40,000, and so on. In this case, the frequency of each bin is simply the number of people with incomes in that bin. 4) Make a frequency table of the following test scores, using the given bins: 76 80 78 76 94 75 98 77 84 88 81 72 91 72 74 86 79 88 72 75 Scores Frequency Relative Frequency Cumulative Frequency 70 to 74 75 to 79 80 to 84 85 to 89 90 to 94 95 to 99 Total
Bar Graphs and Pie Charts Bar graphs and pie charts are commonly used to show data when the categories are qualitative. Bar graphs can display frequency and or relative frequency fairly easily Pie charts are primarily used for relative frequencies (total pie is 100%) Important Labels for Most Graphs: Title: This explains what is being shown. Vertical scale and title: Numbers on the vertical axis should clearly indicate the scale. The numbers should line up with the tick marks. Include a label that describes the variable on the vertical axis. Horizontal scale and title: The categories should be clearly indicated along the horizontal axis. Use tick marks if the categories are quantitative. Include a label that describes the variable on the horizontal axis. Legend: If multiple data sets are displayed on a single graph, include a legend or key to identify the individual data sets. Bar Graph of Example #1 Pie Chart of Example #1
5-6 Fifty students were asked What s your favorite color? Make a bar graph and a pie chart from the results given below: Color Frequency Black 15 Blue 10 Pink 6 Red 19 Histograms and Line Charts Histograms and line charts are commonly used to show data when the categories are quantitative. A histogram is a bar graph used for quantitative data categories. In most histogram, the categories are binned. The width of the bar represents the range of the bin. There are no gaps between the bars of a histogram. A line chart (also called a frequency polygon) serves the same purpose as a histogram, but instead of using bars, a line chart connects a series of dots. When data are binned, the dot is placed at the center of each bin. A line chart can easily be made from a histogram by connecting the top midpoints of each bar of a histogram. (* When data is binned using Excel, Excel will place the dots at the upper bounds of the bins.) Histogram of #4 Line Chart of #4
7-8 Make a histogram and line chart of the following: Age of Award Winning Actresses Age of Academy Award Winning Actresses Age Number of Academy award winning actresses 20-29 28 30-39 34 40-49 12 50-59 1 60-69 5 70-79 1 80-89 1 frequenc y 40 30 20 10 20 30 40 50 60 70 80 90 Age at time of award Time-Series Diagrams A times-series diagram is a line chart or a histogram in which the horizontal axis represents time. A time-series diagram shows how a variable changes with time. 9) The following figure shows a time-series line chart of stock, bond, and gold prices over a 12- week period. Suppose that, on July 7, you invested $100 in a stock fund that tracks the S&P 500, $100 in a bond fund that follows the Treasury Bond Index, and $100 in gold. If you sold all three funds on August 4, how much did you gain or lose?
10-13 What type of graph would you use for the following? (Pie chart, histogram, line chart, or bar graph) 10) Data about favorite basketball teams (the Suns of course!). 11) Data about college major (math of course!). 12) Data about the number of hours students spend on Facebook. 13) Data about the median price of a house in Chandler from 1960-2000.