Lecture Presentation Slides SEVENTH EDITION STATISTICSMoore / McCabe / Craig Introduction to the Practice of Chapter 1 Looking at Data: Distributions

2 Chapter 1 Looking at Data: Distributions Introduction 1.1 Displaying Distributions with Graphs 1.2 Describing Distributions with Numbers 1.3 Density Curves and Normal Distributions

Variables We construct a set of data by first deciding which cases or units we want to study. For each case, we record information about characteristics that we call variables. Individual An object described by data Variable Characteristic of the individual Categorical Variable Places individual into one of several groups or categories. Quantitative Variable Takes numerical values for which arithmetic operations make sense. 3

Distribution of a Variable 4 To examine a single variable, we graphically display its distribution.The distribution of a variable tells us what values it takes and how often it takes these values. Distributions can be displayed using a variety of graphical tools. The proper choice of graph depends on the nature of the variable. Categorical Variable Pie chart Bar graph Quantitative Variable Histogram Stemplot

Categorical Variables 5 The distribution of a categorical variablelists the categories and gives the count or percent of individuals who fall into that category. Pie Charts show the distribution of a categorical variable as a “pie” whose slices are sized by the counts or percents for the categories. Bar Graphs represent each category as a bar whose heights show the category counts or percents.

Pie Charts and Bar Graphs 6 MaterialWeight (million tons)Percent of totalFood scraps 25.9 11.2% Glass 12.8 5.5% Metals 18.0 7.8% Paper, paperboard 86.7 37.4% Plastics 24.7 10.7% Rubber, leather, textiles 15.8 6.8% Wood 12.7 5.5% Yard trimmings 27.7 11.9% Other 7.5 3.2% Total 231.9 100.0%

Quantitative Variables 7 The distribution of a quantitative variable tells us what values the variable takes on and how often it takes those values. Histograms show the distribution of a quantitative variable by using bars whose height represents the number of individuals who take on a value within a particular class. Stemplots separate each observation into a stem and a leaf that are then plotted to display the distribution while maintaining the original values of the variable. Time plots plot each observation against the time at which it was measured.

8 To construct a stemplot: Separate each observation into a stem(first part of the number) and a leaf(the remaining part of the number). Write the stems in a vertical column; draw a vertical line to the right of the stems. Write each leaf in the row to the right of its stem; order leaves if desired. Stemplots

Example: Weight Data ― Introductory Statistics Class192110195152120170135185120110165185128212175180119203260165185170210123165186139150100106Key 20|3 means 203 pounds Stems = 10s Leaves = 1s10 0166 11 009 12 0034578 13 00359 14 08 15 00257 16 555 17 000255 18 000055567 19 245 20 3 21 025 22 0 23 24 25 26 0 Stems Leaves 2 2 5 Stemplots 9

10 If there are very few stems (when the data cover only a very small range