Looking at data Visualization tools

Goals for sections 1.1-1.2 Organize data and break it down into manageable pieces. Learn the terminology for discussing data. Describe patterns and identify peculiarities. Use graphs and numerical summaries.

Individuals A data set contains information about individuals (people, objects, experimental subjects, etc.). In a typical grading spreadsheet, the students in the class are the individuals; each student is typically assigned one row in the spreadsheet.

Variables A variable describes some characteristic of an individual. Each variable has its own column in our spreadsheet. Variables could include: name, class year, number of absences, homework grade average, midterm test score, etc.

Questions to ask yourself What individuals are described? How many are there? Exactly what do the variables describe, and in what units? How many variables are there? How and by whom were the data collected? Are the variables appropriate for answering questions of interest?

Descriptive statistics Statistics that we see in the media and other everyday sources are usually descriptive statistics. Descriptive statistics are summaries of data. They include charts, graphs and summary statistics (mean, standard deviation, etc.).

Categorical (Qualitative) Variables Records which category an individual belongs to. Qualitative variables can be nominal or ordinal. Nominal example: gender Ordinal example: class (fresh., soph., jr., sr.) Arithmetic operations cannot be performed on these values in a way that makes sense.

Quantitative variables Take on numerical values. Quantitative variables can be continuous or discrete. Continuous example: Body weight Discrete example: Size of family Arithmetic operations can be performed on these values in a way that makes sense.

Distributions Tell which values a variable can take, and how often the variable take that value. The distribution of age groups in the U.S. population is (based on 1999 data): Under 18: 25.7% 18-64 years: 61.6% Over 65 and over: 12.7% The distribution of gender in the U.S. population is (based on 2000 data): Female: 143.4 mil Male: 138.1 mil

Graphs for qualitative variables Pie chart: A circle (“pie”) represents all the individuals. “Slices” represent the number or percentage of individuals in each category. Bar graph/chart: Number or percentage of individuals in each category represented by bars of differing heights. Use the data provided by the class (such as major or class year) to demonstrate how to use Minitab to make these graphs. Make sure to find out whether Minitab will allow re-ordering of the bars (for ordinal variables).

Graphs for quantitative variables Histogram Bars represent the number or percentage of individuals in a certain numerical range of the variable Stemplot (or “stem-and-leaf” plot) Similar to a sideways histogram and is easily done with pencil and paper Use data from students to draw stemplot or histograms. (Perhaps heights or haircuts or town populations.)

Describing distributions using graphs Get an idea of the overall pattern and notice which, if any, observations deviate from it. (These are called outliers). Unimodal (1 peak)? Bimodal (2 peaks)? Symmetric? Right-skewed (right tail longer than left)? Left-skewed (left tail longer than right)? Note the center and spread of the distribution.

Dealing with more than one quantitative variable Time plot (or “time series” plot) Values are plotted on y axis with the time of observation on the x axis. Back-to-back stemplot Easy to do with pencil and paper, but Minitab won’t make them. Stacked histograms Use relative frequencies rather than counts and same axes to facilitate comparisons. Use marathon data in exercise 1.38 on pg. 38 for time series. Use height data for men and women to draw back-to-back stemplots and stacked histograms.