Statistics Chapter 1: Exploring Data

1.1 Displaying Distributions with Graphs Individuals Objects that are described by a set of data Variables Any characteristic of an individual Types of variables Categorical variables Record which of several groups or categories to which an individual belong Quantitative variables Take numerical values on which arithmetical operations can be performed

Distribution of variable: values are taken by the variable and the frequency of the values Charts representing data Bar chart Pie chart Dot plot Histogram Stemplots timeplots

Distributions Description of overall pattern: center?? spread?? shape?? symmetry?? outliers?? skewed??

1.2 Describing Distributions with Numbers Measuring Center The MEAN The MEDIAN The MODE Measuring Spread or Variability Quartiles Standard Deviation s

Other Measurements Interquartile range IQRQ3 – Q1 RangeMax – Min Outliers

Other Measurements Five Number Summary: Minimum, Q1, Median, Q3, Maximum Boxplot, Modified Boxplot, Side-by- side boxplots

Properties of the Standard Deviation s measures spread by looking at how far the observations are from their mean. Used when mean is chosen as the measure of center If there is no spread, s = 0. This means that all observations have the same value. Strongly influenced by extreme values. s 2 is called variance.