Transcript Introduction to Statistics I - Department of Mathematics and Statistics

Introduction to Statistics I
MATH 1131, Summer I 2008,
Department of Math. & Stat.,
York University
Goal of the course
 Understanding
the need for statistical
techniques
 Introduction
 Able
to basic concepts
to summarize and analyze data with
some basic statistical skills
TextBook
Introduction to
Statistics and Data
Analysis,
3rd Edition, Peck,
Olsen and Pevore.
We will cover roughly the
first 10 chapters.
Timeline

6 week course, from May 6, 2008 to June 12,
2008

6 hours per week, Tuesdays and Thursdays,
6 - 9 pm. CSE “B”

Tutorial: one hour before each class

Final Exam: June 18 – 20, 2008
Course webpage

http://math.yorku.ca/~jnliu/Syllabus_Math1131_2008.htm
Assignments, solutions, and other announcements will be
posted on the webpage.
Course Description
 Displaying
and describing distributions
 relations between variables
 Simpson's paradox and the need for
design
 Experimental design and sampling design,
randomization
Course Description
 Probability
models and random variables,
mean and variance
 Basic laws of probability
 Probability distribution - binomial
distribution and the normal distribution.
 The Central Limit Theorem
 Inference including confidence intervals
and test of significance
Evaluation

4 Assignments, 5% each
2
Quizzes, 5% each
 Midterm,
 Final
30%
Exam, 40%
Mean
 We
have a data set with n data points
X_1, X_2, … X_n
 The
MEAN of this data set is defined as
(X_1+x_2+…X_n)/n
Suppose the value of the mean is m.
Variance
– m)^2
 (x_2 – m)^2
…
 (X_n - m)^2
 Sum of those numbers /(n-1) is called the
variance.
 Take the square root, you will get the
standard deviation.
 (x_1
What are they for?
 Mean
describes the center of the data
 Variance
or standard deviation describes
the degree of spread of the data
 Together
they give a simple summary of
the information from the data
Example
 Result
of the final exam
 The
class mean is 75, with a standard
deviation of 15
 Grades
more than 90 or less than 60 are
considered one standard deviation away
from the mean, therefore extremely well or
poor.
display data graphically
 Bar
chart
 Pie
chart
5-number summary
5-number:
Minimum
Maximum
Q1: the first quartile
Median
Q3: the third quartile

Median
 Median:
the “middle point” of the data set,
such that half of the data points are bigger
than it, and the other half are smaller than
it.
 How
to find the median:
Sort the data
Take the data point in the middle
Boxplot
Side by side boxplot
Histogram