Elementary Statistics, 13e - Sybil Nelson

Elementary Statistics, 13e - Sybil Nelson

Elementary Statistics Thirteenth Edition Chapter 2 Summarizing and Graphing Data Copyright 2018, 2014, 2012 Pearson Education, Inc. All Rights Reserved Summarizing and Graphing Data

2-1 Frequency Distributions for Organizing and Summarizing Data 2-2 Histograms 2-3 Graphs that Enlighten and Graphs that Deceive 2-4 Scatterplots, Correlation, and Regression Copyright 2018, 2014, 2012 Pearson Education, Inc. All Rights Reserved Key Concept While a frequency distribution is a useful tool for

summarizing data and investigating the distribution of data, an even better tool is a histogram, which is a graph that is easier to interpret than a table of numbers. Copyright 2018, 2014, 2012 Pearson Education, Inc. All Rights Reserved Histogram Histogram A graph consisting of bars of equal width drawn adjacent to each other (unless there are gaps in the data)

The horizontal scale represents classes of quantitative data values, and the vertical scale represents frequencies. The heights of the bars correspond to frequency values. Copyright 2018, 2014, 2012 Pearson Education, Inc. All Rights Reserved Important Uses of a Histogram Visually displays the shape of the distribution of the data

Shows the location of the center of the data Shows the spread of the data Identifies outliers Copyright 2018, 2014, 2012 Pearson Education, Inc. All Rights Reserved Relative Frequency Histogram Relative Frequency Histogram It has the same shape and horizontal scale as a histogram, but the vertical scale is marked with

relative frequencies instead of actual frequencies. Time (seconds) Frequency 75-124 11

125-174 24 175-224 10 225-274

3 275-324 2 Copyright 2018, 2014, 2012 Pearson Education, Inc. All Rights Reserved Critical Thinking Interpreting Histograms

Explore the data by analyzing the histogram to see what can be learned about CVDOT: the Center of the data, the Variation, the shape of the Distribution, whether there are any Outliers, and Time. Copyright 2018, 2014, 2012 Pearson Education, Inc. All Rights Reserved

Common Distribution Shapes Copyright 2018, 2014, 2012 Pearson Education, Inc. All Rights Reserved Normal Distribution Because this histogram is roughly bell-shaped, we say that the data have a normal distribution. Copyright 2018, 2014, 2012 Pearson Education, Inc. All Rights Reserved

Skewness (1 of 3) Skewness A distribution of data is skewed if it is not symmetric and extends more to one side than to the other. Copyright 2018, 2014, 2012 Pearson Education, Inc. All Rights Reserved Skewness (2 of 3) Data skewed to the right (positively skewed) have a longer right tail.

Copyright 2018, 2014, 2012 Pearson Education, Inc. All Rights Reserved Skewness (3 of 3) Data skewed to the left (negative skewed) have a longer left tail. Copyright 2018, 2014, 2012 Pearson Education, Inc. All Rights Reserved Assessing Normality with Normal

Quantile Plots (1 of 5) Criteria for Assessing Normality with a Normal Quantile Plot Normal Distribution: The pattern of the points in the normal quantile plot is reasonably close to a straight line, and the points do not show some systematic pattern that is not a straight-line pattern. Copyright 2018, 2014, 2012 Pearson Education, Inc. All Rights Reserved

Assessing Normality with Normal Quantile Plots (2 of 5) Criteria for Assessing Normality with a Normal Quantile Plot Not a Normal Distribution: The population distribution is not normal if the normal quantile plot has either or both of these two conditions: The points do not lie reasonably close to a straight-line pattern. The points show some systematic pattern that is not a

straight-line pattern. Copyright 2018, 2014, 2012 Pearson Education, Inc. All Rights Reserved Assessing Normality with Normal Quantile Plots (3 of 5) Normal Distribution: The points are reasonably close to a straight-line pattern, and there is no other systematic pattern that is not a straight-line pattern.

Copyright 2018, 2014, 2012 Pearson Education, Inc. All Rights Reserved Assessing Normality with Normal Quantile Plots (4 of 5) Not a Normal Distribution: The points do not lie reasonably close to a straight line. Copyright 2018, 2014, 2012 Pearson Education, Inc. All Rights Reserved

Assessing Normality with Normal Quantile Plots (5 of 5) Not a Normal Distribution: The points show a systematic pattern that is not a straight-line pattern. Copyright 2018, 2014, 2012 Pearson Education, Inc. All Rights Reserved

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