Chapter 3: The Normal Distribution
MATH 1013: Elements of Statistics
Spring 2015
Temple University
Chapter 3: The Normal Distribution
Introduction
In Chapter 1, we looked at visualizing data for quantitative variables using a
histogram. For data sets with
10 1
Ch 5 Random Variables (r.v.)
Suppose S and T are sets. A function f assigns to each
element in s in S a unique element in t in T
: , f(s) = t
f(s) is called the image of s under f.
The set of all the image points, f(S) is called the range
of f.
= (
71
PROBABILITY
The mathematics of phenomenon of chance or randomness
Definitions:
A random experiment is an occurrence with a result or outcome that is uncertain before the
experiment takes place.
The set of all possible outcomes is called the sample spac
8 1 Theorems on Probability
1.
2.
3.
4.
5.
P(null set) = 0
If , () ()
\B =
= +
= + +
+
82
Discrete probability
A probability model where the sample space is finite
or countably infinite.
Example (finite): Let three coins be tossed
S = number of h
91
Ch 4- Conditional Probability
Suppose A and E are events in a sample space S and P(E)>0. The
conditional probability of A given E, denoted as (|), is the probability
that an event A occurs given E has occurred.
( )
=
()
Example: It is well known th
Ch 6 - BINOMIAL and NORMAL
DISTRIBUTIONS
11 1
Bernoulli Trials
Binomial Distribution
Normal Distribution
Central Limit Theorem
Normal Approximation to the Binomial
11 2 REPEATED BERNOULLI TRIALS AND THE
BINOMIAL RANDOM VARIABLE
The General Formula
3 1 OUTLIERS IN DATA SETS Suspected and
Otherwise
Data values that are extremely high (or low) in relation to the
rest of the values cause some concern. A measure of how
extreme is a high or low value is defined in terms of the
Inter Quartile Range (IQR)
41
CHANGING THE UNIT OF MEASUREMENT
Standardization From x to z The Most Important Linear
Standardization:
Transformation
z = x -s x or z = x -s m
Example: An elementary school class ran 1 mile with a mean of 11 minutes
and a standard deviation of 3 minut
Scatter
Plot,
Quadrant
Plot,
Least
Squares
51
Regression Line, Linear Correlation Coefficient
A Comprehensive Example
Samanthas parents are concerned that she seems short for her age. Their
doctor has the following record of Sams height:
Age (months)
36
21
SUMMARIZING DATA: MEASURES OF
POSITION
Measures of position help identify the relative
standing of a data value within a data set or in
comparison to data values from other data sets.
The median of a data set is the most prominent
example of a measure
1 1
TWO ASPECTS OF STATISTICS
(Covered In Our Course)
1. Descriptive Statistics
2. Inferential Statistics
1 - 2
The Missing Aspect:
Data Collection and
Sampling Methods
(One exception: Simple Random Sampling)
1 - 3
Population and Sample
Data* may stand
Chapter 4: Scatterplots and Correlations
MATH 1013: Elements of Statistics
Spring 2015
Temple University
Chapter 4: Scatterplots and Correlations
Introduction
In Chapters 1-3, we analyzed data for a single variable. When data is collected
or measured for
MATH 1013, Elements of Statistics
Spring 2015
Answers to Even-numbered Problems
Chapter 1 (For Chapter 1 problems, do not worry about questions regarding center and spread)
14 C
16 B
18 B
20 C
22 C
9
30 Data is skewed to the right; 6 servings per day: 74
Chapter 2: Describing Distributions with Numbers
MATH 1013: Elements of Statistics
Spring 2015
Temple University
Chapter 2: Describing Distributions with Numbers
Introduction
In Chapter 1, we discussed investigating variables graphically. In Chapter 2, we
Chapter 1: Picturing Distributions with Graphs
MATH 1013: Elements of Statistics
Spring 2015
Temple University
Chapter 1: Picturing Distributions with Graphs
Introduction
Statistics is the science of data
Example: Google, Facebook, Amazon collect a large
TEMPLE UNIVERSITY
DEPARTMENT OF MATHEMATICS
MATH 1013, Elements of Statistics
Spring 2015
Course Time and Location
TR 3:30 PM 4:50 PM, Beury Hall 166
Course Instructor
Matt Zumbrum (please call me Matt)
Wachman Hall 1014
[email protected] (preferred meth
MATH 1013 SYLLABUS Fall 2013
Instructor
Dr. R. (Alu) Srinivasan
510 Wachman Hall
[email protected]
Office Hours TTH 3:30 pm 5:00 pm, by appointment
Classroom
BE160
Class Time TTH 2:00 3:20
Text
Introduction to Probability and Statistics, by Lipschutz and S