Introduction to Statistics IIntroduction to Statistics I

MATH 1131, Summer I 2008, MATH 1131, Summer I 2008,

Department of Math. & Stat., Department of Math. & Stat.,

York UniversityYork University

Goal of the courseGoal of the course

Understanding the need for statistical Understanding the need for statistical techniquestechniques

Introduction to basic concepts Introduction to basic concepts

Able to summarize and analyze data with Able to summarize and analyze data with some basic statistical skillssome basic statistical skills

TextBookTextBook

Introduction to Introduction to Statistics and Data Statistics and Data Analysis, Analysis,

3rd Edition, Peck, 3rd Edition, Peck, Olsen and Pevore. Olsen and Pevore.

We will cover roughly the We will cover roughly the first 10 chapters.first 10 chapters.

TimelineTimeline

6 week course, from May 6, 2008 to June 12, 6 week course, from May 6, 2008 to June 12, 20082008

6 hours per week, Tuesdays and Thursdays, 6 hours per week, Tuesdays and Thursdays, 6 - 9 pm. CSE “B”6 - 9 pm. CSE “B”

Tutorial: one hour before each classTutorial: one hour before each class

Final Exam: June 18 – 20, 2008Final Exam: June 18 – 20, 2008

Course webpageCourse webpage

http://math.yorku.ca/~jnliu/Syllabus_Math1131_2008.htmhttp://math.yorku.ca/~jnliu/Syllabus_Math1131_2008.htm

Assignments, solutions, and other announcements will be Assignments, solutions, and other announcements will be posted on the webpage. posted on the webpage.

Course Description Course Description

Displaying and describing distributionsDisplaying and describing distributions relations between variables relations between variables Simpson's paradox and the need for Simpson's paradox and the need for

design design Experimental design and sampling design, Experimental design and sampling design,

randomization randomization

Course DescriptionCourse Description

Probability models and random variables, Probability models and random variables, mean and variance mean and variance

Basic laws of probability Basic laws of probability Probability distribution - binomial Probability distribution - binomial

distribution and the normal distribution. distribution and the normal distribution. The Central Limit Theorem The Central Limit Theorem Inference including confidence intervals Inference including confidence intervals

and test of significance and test of significance

EvaluationEvaluation

4 Assignments, 5% each4 Assignments, 5% each

2 Quizzes, 5% each2 Quizzes, 5% each

Midterm, 30%Midterm, 30%

Final Exam, 40%Final Exam, 40%

MeanMean

We have a data set with n data points We have a data set with n data points X_1, X_2, … X_nX_1, X_2, … X_n

The MEAN of this data set is defined asThe MEAN of this data set is defined as

(X_1+x_2+…X_n)/n(X_1+x_2+…X_n)/n

Suppose the value of the mean is m.Suppose the value of the mean is m.

VarianceVariance

(x_1 – m)^2 (x_1 – m)^2 (x_2 – m)^2(x_2 – m)^2 …… (X_n - m)^2(X_n - m)^2 Sum of those numbers /(n-1) is called the Sum of those numbers /(n-1) is called the

variance.variance. Take the square root, you will get the Take the square root, you will get the

standard deviation.standard deviation.

What are they for?What are they for?

Mean describes the center of the dataMean describes the center of the data

Variance or standard deviation describes Variance or standard deviation describes the degree of spread of the datathe degree of spread of the data

Together they give a simple summary of Together they give a simple summary of the information from the data the information from the data

ExampleExample

Result of the final examResult of the final exam

The class mean is 75, with a standard The class mean is 75, with a standard deviation of 15deviation of 15

Grades more than 90 or less than 60 are Grades more than 90 or less than 60 are considered one standard deviation away considered one standard deviation away from the mean, therefore extremely well or from the mean, therefore extremely well or poor.poor.

display data graphicallydisplay data graphically

Bar chartBar chart

Pie chart Pie chart

5-number summary5-number summary

5-number:5-number:

MinimumMinimum

MaximumMaximum

Q1: the first quartileQ1: the first quartile

MedianMedian

Q3: the third quartileQ3: the third quartile

MedianMedian

Median: the “middle point” of the data set, Median: the “middle point” of the data set, such that half of the data points are bigger such that half of the data points are bigger than it, and the other half are smaller than than it, and the other half are smaller than it.it.

How to find the median:How to find the median:

Sort the data Sort the data

Take the data point in the middleTake the data point in the middle

BoxplotBoxplot

Side by side boxplotSide by side boxplot

HistogramHistogram