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

x

Other Measurements

Interquartile rangeIQR Q3 – Q1

Range Max – Min

OutliersQ3 1 5 IQR.

Q1 1 5 IQR.

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. s2 is called variance.