Chapter 5: Statistical Reasoning
Assignment #3: Unit 5C
Statistical Tables and Graphs
Pages 349 - 359
1. What is a frequency table? Explain what we mean by the categories and frequencies. What do we mean by relative frequency? What do we mean by cumulative frequency?
A better way to display data is with a frequency table – a table showing the number of times, or frequencies, that each grade appears. The five possible grades are called the categories for the table.
There are 2 common variations on the idea of frequency. The relative frequency for a category expresses its frequencies as a fraction or percentage of the total.
The cumulative frequency is the number of responses in a particular category and all preceding categories.
2. What is the distinction between qualitative data and quantitative data? Give a few examples of each.
Qualitative data describe qualities or nonnumerical categories.
Quantitative data represent counts or measurements.
Example: Classify each of the following types of data as wither qualitative or quantitative:
a. Brand names of shoes in a consumer survey. Non numerical categories = Qualitative Data
b. Heights of students measurements = Quantitative data
c. Audience ratings of a film on a scale of 1 to 5, where 5 means excellent. Qualitative data
3. What is the purpose of binning? Give an example in which binning is useful.
When we deal with quantitative data categories, it’s often useful to group, or bin, the data into categories that cover a range of possible values. For example, in a table of income levels, it might be useful to create bins of $0 to $20,000, $20,001 t0 $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. What two types of graphs are most common when the categories are qualitative data? Describe the construction of each.
Bar graphs and pie charts are commonly used to show data when the categories are qualitative.
See class examples for each type.
5. Describe the importance of labeling on a graph, and briefly discuss the kinds of labels that should be included on graphs.
Nowadays, most people make graphs with the aid of computers that measure bar lengths or wedge sizes automatically. However, you must still specify any labels or axis marks you want on a graph. This labeling is extremely important: without proper labels, a graph is meaningless.
Important Labels for Graphs:
Title/Caption: The graph should have a title or caption 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 – the marks along the axis that precisely locate the numerical values. Include a label that describes the variable shown on the horizontal axis.
Horizontal scale and title: The categories should be clearly indicated along the horizontal axis. Include a label that describes the variable shown 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.
6. What two types of graphs are most common when the categories are quantitative data? Describe the construction of each.
For quantitative data categories, the two most common types of graphics are histograms and line charts.
See examples illustrated in class.
Exercises in your textbook: Pages 360 – 361 Problems 17 - 46