MM07 StatisticsMM07 StatisticsWelcome to the Unit 3 Seminar

Dr. Bob

Available Resources If You Need Help

• Math and Writing Centers—under My Studies Tab on your home page. Live Free Tutoring available for Stats• Sunday: 8:00 PM to 12:00 AM ET • Monday: 11:00 AM to 4:00 PM ET; 8:00 PM to

12:00 AM ET• Tuesday: 11:00 AM to 4:00 PM ET; 8:00 PM to

12:00 AM ET• Wednesday: 11:00 AM to 4:00 PM ET; 8:00 PM

to 12:00 AM ET• Thursday: 11:00 AM to 4:00 PM ET; 8:00 PM to

12:00 AM ET

Frequency Tables

A basic frequency table has two columns:

• One column lists all the categories of data.

• The other column lists the frequency of each category, which is the number of data values in the category.

Frequency Table Example

Binning Data• When it is impossible or impractical to have a

category for every value in a data set, we bin (or group) the data into categories (bins), each covering a range of possible data values.

Relative FrequencyThe relative frequency of any category is the proportion or percentage of the data values that fall in that category:

relative frequency = frequency in category total frequency

Cumulative FrequencyThe cumulative frequency of any category is the number of data values in that category and all preceding categories

Distributions• The distribution of a variable refers to the

way its values are spread over all possible values. We can summarize a distribution in a table or show a distribution visually with a graph.

Bar Graphs• A bar graph is one of the simplest ways to

picture a distribution. Bar graphs are commonly used for qualitative data or discrete data.

• Each bar represents the frequency (or relative frequency) of one category: the higher the frequency, the longer the bar. The bars can be either vertical or horizontal.

Vertical Bar Graph

Dotplot• A dotplot is a variation on a bar graph in which

we use dots rather than bars to represent the frequencies. Each dot represents one data value.

Pareto ChartA bar graph in which the bars are arranged in frequency order is often called a Pareto chart.

Pie ChartsPie charts are usually used to show relative frequency distributions. A circular pie represents the total relative frequency of 100%, and the sizes of the individual slices, or wedges, represent the relative frequencies of different categories. Pie charts are used almost exclusively for qualitative data.

Histograms• A graph in which the bars have a natural order and

the bar widths have specific meaning, is called a histogram.

• The bars in a histogram touch each other because there are no gaps between the categories, the data are continuous

Stem-and-Leaf PlotThe stem-and-leaf plot (or stemplot) looks somewhat like a histogram turned sideways, except in place of bars we see a listing of data for each category.

Line ChartsA line chart shows a distribution of quantitative data as a series of dots connected by lines. For each dot, the horizontal position is the center of the bin it represents and the vertical position is the frequency value for the bin.

Time-Series Diagram

A histogram or line chart in which the horizontal axis represents time is called a time-series diagram

DistortionsThe lengths of the bars represent the data, but our eyes tend to focus on the areas of the bars. For example, the right bar is supposed to show that a dollar in 2006 was worth 41% as much as a dollar in 1980. Its length is indeed 41% of that of the left bar, but its area is much smaller in comparison (about 17% of the area of the left bar).

Figure 3.38 The lengths of the dollars are proportional to their spending power, but our eyes are drawn to the areas, which decline more than the lengths.

Distortions

StatCrunch Graphics

QUESTIONS?