Download Quantitative Data

Lecture Slides
Elementary Statistics
Twelfth Edition
and the Triola Statistics Series
by Mario F. Triola
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 1.1-‹#›
Preview
Polls, studies, surveys and other data
collecting tools collect data from a small part
of a larger group so that we can learn
something about the larger group.
This is a common and important goal of
statistics: Learn about a large group by
examining data from some of its members.
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 1.1-‹#›
Preview
In this context, the terms sample and
population have special meaning. Formal
definitions for these and other basic terms
will be given here.
In this chapter, we will look at some of the
ways to describe data.
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 1.1-‹#›
Chapter 1
Introduction to Statistics
1-1
Review and Preview
1-2
Statistical and Critical Thinking
1-3
Types of Data
1-4
Collecting Sample Data
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 1.1-‹#›
Data
 Data Collections of observations, such as
measurements, genders, or survey
responses
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 1.1-‹#›
Statistics
 Statistics The science of planning studies and
experiments, obtaining data, and then
organizing, summarizing, presenting,
analyzing, interpreting, and drawing
conclusions based on the data
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 1.1-‹#›
Population
 Population The complete collection of all
measurements or data that are being
considered
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 1.1-‹#›
Census versus Sample

Census Collection of data from every
member of a population

Sample Subcollection of members selected
from a population
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 1.1-‹#›
Potential Pitfalls – Misleading
Conclusions 1-2
 Concluding that one variable causes the
other variable when in fact the variables are
only correlated or associated together.
Two variables that may seemed linked, are
smoking and pulse rate.
We cannot conclude the one causes the
other. Correlation does not imply causality.
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 1.2-‹#›
Chapter 1
Introduction to Statistics
1-1
Review and Preview
1-2
Statistical and Critical Thinking
1-3
Types of Data
1-4
Collecting Sample Data
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 1.3-‹#›
Parameter
 Parameter
a numerical measurement describing
some characteristic of a population.
population
parameter
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 1.3-‹#›
Statistic
 Statistic
a numerical measurement describing
some characteristic of a sample.
sample
statistic
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 1.3-‹#›
Quantitative Data
 Quantitative (or numerical) data
consists of numbers representing counts or
measurements.
Example: The weights of supermodels
Example: The ages of respondents
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 1.3-‹#›
Categorical Data
Categorical (or qualitative or
attribute) data
consists of names or labels (representing
categories).
Example: The gender (male/female) of
professional athletes
Example: Shirt numbers on professional athletes
uniforms - substitutes for names.
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 1.3-‹#›
Working with Quantitative Data
Quantitative data can be further
described by distinguishing between
discrete and continuous types.
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 1.3-‹#›
Discrete Data

Discrete data
result when the number of possible values is
either a finite number or a ‘countable’ number
(i.e. the number of possible values is
0, 1, 2, 3, . . .).
Example: The number of eggs that a hen lays
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 1.3-‹#›
Continuous Data
 Continuous (numerical) data
result from infinitely many possible values that
correspond to some continuous scale that
covers a range of values without gaps,
interruptions, or jumps.
Example: The amount of milk that a cow
produces; e.g. 2.343115 gallons per day
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 1.3-‹#›
Summary - Levels of Measurement
 Nominal - categories only
 Ordinal - categories with some order
 Interval - differences but no natural zero point
 Ratio - differences and a natural zero point
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 1.3-‹#›
Methods of Sampling – Summary
1-4
 Random
 Systematic
 Convenience
 Stratified
 Cluster
 Multistage
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 1.4-‹#›
Preview Ch 2
Characteristics of Data
1. Center: A representative value that indicates where the
middle of the data set is located.
2. Variation: A measure of the amount that the data values
vary.
3. Distribution: The nature or shape of the spread of data
over the range of values (such as bell-shaped, uniform,
or skewed).
4. Outliers: Sample values that lie very far away from the
vast majority of other sample values.
5. Time: Changing characteristics of the data over time.
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 2.1-‹#›
Ch 2-3 Example
IQ scores from children with low levels of lead.
IQ Score
Frequency
50-69
2
70-89
33
90-109
35
110-129
7
130-149
1
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 2.3-‹#›
Ch 2-3 Skewness
A distribution of data is skewed if it is not
symmetric and extends more to one side to the
other.
Data skewed to the right (positively skewed)
have a longer right tail.
Data skewed to the left (negative skewed)
have a longer left tail.
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 2.3-‹#›
Example – Discuss the Shape
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 2.3-‹#›
Ch 2-4 Pareto Chart
A bar graph for qualitative data, with the bars arranged in
descending order according to frequencies
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 2.4-‹#›
Ch 2-4 Pie Chart
A graph depicting qualitative data as slices of a circle, in which the
size of each slice is proportional to frequency count
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 2.4-‹#›
Ch 2-4 Frequency Polygon
uses line segments connected to points directly above class
midpoint values.
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 2.4-‹#›
Ch 2-4 Important Principles
Suggested by Edward Tufte
For small data sets of 20 values or fewer, use a table instead of a
graph.
A graph of data should make the viewer focus on the true nature of
the data, not on other elements, such as eye-catching but distracting
design features.
Do not distort data. Construct a graph to reveal the true nature of the
data.
Almost all of the ink in a graph should be used for the data, not for
the other design elements.
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 2.4-‹#›
Ch 3 Preview
 Descriptive Statistics
In this chapter we’ll learn to summarize or
describe the important characteristics of a
data set (mean, standard deviation, etc.).
 Inferential Statistics
In later chapters we’ll learn to use sample
data to make inferences or generalizations
about a population.
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 3.1-‹#›
Ch 3-3 Definition
The standard deviation of a set of
sample values, denoted by s, is a
measure of how much data values
deviate away from the mean.
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 3.3-‹#›
Ch 3-3 Sample Standard
Deviation Formula
( x  x )
s
n 1
2
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 3.3-‹#›
Ch 3-3 Standard Deviation –
Important Properties
 The standard deviation is a measure of variation
of all values from the mean.
 The value of the standard deviation s is usually
positive (it is never negative).
 The value of the standard deviation s can
increase dramatically with the inclusion of one or
more outliers (data values far away from all
others).
 The units of the standard deviation s are the same
as the units of the original data values.
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 3.3-‹#›
Ch 3-3 Example
Use either formula to find the standard
deviation of these numbers of chocolate
chips:
22, 22, 26, 24
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 3.3-‹#›
Ch 3-3 Example
s
 x  x 
2
n 1
 22  23.5   22  23.5   26  23.5   24  23.5
2

2
2
2
4 1
11

 1.9149
3
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 3.3-‹#›
Ch 3-3
Empirical (or 68-95-99.7) Rule
For data sets having a distribution that is
approximately bell shaped, the following properties
apply:
 About 68% of all values fall within 1 standard
deviation of the mean.
 About 95% of all values fall within 2 standard
deviations of the mean.
 About 99.7% of all values fall within 3 standard
deviations of the mean.
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 3.3-‹#›
Ch 3-3 The Empirical Rule
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 3.3-‹#›
Ch3-3 Coefficient of Variation
The coefficient of variation (or CV) for a set of
nonnegative sample or population data,
expressed as a percent, describes the
standard deviation relative to the mean.
Sample
s
cv   100%
x
Population

cv   100%

Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 3.3-‹#›
Ch 3-4 z score
z
Score (or standardized value)
the number of standard deviations that a given
value x is above or below the mean
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 3.4-‹#›
Measures of Position z Score
Sample
xx
z
s
Population
z
x

Round z scores to 2 decimal places
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 3.4-‹#›
Example
The author of the text measured his pulse rate to
be 48 beats per minute.
Is that pulse rate unusual if the mean adult male
pulse rate is 67.3 beats per minute with a
standard deviation of 10.3?
x  x 48  67.3
z

 1.87
s
10.3
Answer: Since the z score is between – 2 and +2,
his pulse rate is not unusual.
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 3.4-‹#›
Ch 3-4 Boxplot - Construction
1. Find the 5-number summary.
2. Construct a scale with values that include
the minimum and maximum data values.
3. Construct a box (rectangle) extending from
Q1 to Q3 and draw a line in the box at the
value of Q2 (median).
4. Draw lines extending outward from the box
to the minimum and maximum values.
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 3.4-‹#›
Ch 3-4 Boxplots
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 3.4-‹#›
Ch 3-4 Outliers
 An outlier is a value that lies very far away
from the vast majority of the other values
in a data set.
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 3.4-‹#›
Ch 3-4 Important Principles
 An outlier can have a dramatic effect on the
mean and the standard deviation.
 An outlier can have a dramatic effect on the
scale of the histogram so that the true nature of
the distribution is totally obscured.
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 3.4-‹#›
Putting It All Together
 So far, we have discussed several basic tools
commonly used in statistics –

Context of data

Source of data

Sampling method

Measures of center and variation

Distribution and outliers

Changing patterns over time

Conclusions and practical implications
 This is an excellent checklist, but it should not
replace thinking about any other relevant factors.
Copyright © 2014, 2012, 2010 Pearson Education, Inc.
Section 3.4-‹#›