Chapter 2
Descriptive Statistics
Contents
Introduction Qualitative Data Frequency Distribution Graphical Methods Quantitative Data Graphical Methods Numerical Summary Box Plot
2
Qualitative Data
Measurements that cannot be measured on a natural numerical
Descriptive Statistics
Quantitative Data
Quantitative Data
Measurements that can be measured on a natural and meaningful numerical scale Examples:
a) b) c)
SAT score of students The current unemployment rate for 50 states Number of calls made over last we
Descriptive Statistics
Numerical Summary
Summation Notation
Observations in a dataset are denoted by cfw_ x1,x2,x3,x4,.xn ; n = sample size x1 is the first observation, x2 is 2nd obs. and so on. We use xi to denote x1 + x2 + x3 + x4 +.+ xn In particular,
Comparing Mean, Median and Mode
For negatively (left) skewed distributions Mean < Median < Mode
Mean Median
Mode
1
Skewed Right
For positively skewed distributions Mean > Median > Mode
Mode
Mean Median
2
Symmetric Distribution
For symmetric (not skewed) d
Frequency Distribution
Dataset is summarized in a tabular form. Range of the dataset is partitioned into a number of classes of equal width. Frequency distribution table is constructed by counting number of observations (called frequency) in each class an
A Complete Example
The dataset gives ammonia level near an exit ramp of a tunnel tunnel for 8 different days cfw_1.53, 1.50, 1.37, 1.51, 1.55, 1.42, 1.41, 1.48
Mean and SD
Obs 1.53 1.50 1.37 1.51 1.55 1.42 1.41 1.48 11.77
2 Deviation Deviation2
.05875 .02
The Empirical Rule
Sometimes the distribution is symmetric and bell shaped. For these kind of distribution mean and sd together can describe the distribution fairly well. Most of the observations lie near the center or mean of the data. EMPIRICAL RULE sum
Chapter 2
Descriptive Statistics
Contents
Introduction Qualitative Data Frequency Distribution Graphical Methods Quantitative Data Graphical Methods Numerical Summary Box Plot
2
Qualitative Data
Measurements that cannot be measured on a natural numerical
Descriptive Statistics
Quantitative Data
Quantitative Data
Measurements that can be measured on a natural and meaningful numerical scale Examples:
a) b) c)
SAT score of students The current unemployment rate for 50 states Number of calls made over last we
Frequency Distribution
Dataset is summarized in a tabular form. Range of the dataset is partitioned into a number of classes of equal width. Frequency distribution table is constructed by counting number of observations (called frequency) in each class an
Descriptive Statistics
Numerical Summary
Summation Notation
Observations in a dataset are denoted by cfw_ x1,x2,x3,x4,.xn ; n = sample size x1 is the first observation, x2 is 2nd obs. and so on. We use xi to denote x1 + x2 + x3 + x4 +.+ xn In particular,
The Empirical Rule
Sometimes the distribution is symmetric and bell shaped. For these kind of distribution mean and sd together can describe the distribution fairly well. Most of the observations lie near the center or mean of the data. EMPIRICAL RULE sum
Chapter 1
Introduction
Contents
What
is Statistics? Applications Fundamental Elements Types of Data Data Collection
What is Statistics?
Statistics is the Science of collection and analysis of Data.
Various aspects:
Classifying Summarizing Analyzing Inte
A Complete Example
The dataset gives ammonia level near an exit ramp of a tunnel tunnel for 8 different days cfw_1.53, 1.50, 1.37, 1.51, 1.55, 1.42, 1.41, 1.48
Mean and SD
Obs 1.53 1.50 1.37 1.51 1.55 1.42 1.41 1.48 11.77
2 Deviation Deviation2
.05875 .02
Comparing Mean, Median and Mode
For negatively (left) skewed distributions Mean < Median < Mode
Mean Median
Mode
1
Skewed Right
For positively skewed distributions Mean > Median > Mode
Mode
Mean Median
2
Symmetric Distribution
For symmetric (not skewed) d
Chapter 1
Introduction
Contents
What
is Statistics? Applications Fundamental Elements Types of Data Data Collection
What is Statistics?
Statistics is the Science of collection and analysis of Data.
Various aspects:
Classifying Summarizing Analyzing Inte