1 Practical Information 2 Introduction to Statistics Per Bruun - - PowerPoint PPT Presentation

Course 02402 Introduction to Statistics Lecture 1: Introduction to Statistics Per Bruun Brockhoff

DTU Informatics Building 305 - room 110 Danish Technical University 2800 Lyngby – Denmark e-mail: pbb@imm.dtu.dk

Per Bruun Brockhoff (pbb@imm.dtu.dk) Introduction to Statistics, Lecture 1 Spring 2013 1 / 22

Agenda

1 Practical Information 2 Introduction to Statistics 3 Descriptive Statistics: Summary Statistics 4 Software: R

Per Bruun Brockhoff (pbb@imm.dtu.dk) Introduction to Statistics, Lecture 1 Spring 2013 2 / 22 Practical Information

Practical information

Teaching module: Tuesdays 13.00-17.00 Generic weekly agenda:

BEFORE teaching module: Read announced stuff 2 hours long lectures (curriculum of the week) 2 hours of exercises (Mix of: Book, Rnote, online quiz-questions) AFTER teaching module: Test yourself by online exam quiz.

Exam: 4 hour multiple choice

Per Bruun Brockhoff (pbb@imm.dtu.dk) Introduction to Statistics, Lecture 1 Spring 2013 4 / 22 Practical Information

Practical Information

Homepage: 02402.imm.dtu.dk

Note about software R Syllabus, Lecture plan Exercises & solutions Slides Podcasts of lectures (In English AND Danish) Quizzes

Campusnet: www.campusnet.dtu.dk

Messages and (certain) file sharings

Per Bruun Brockhoff (pbb@imm.dtu.dk) Introduction to Statistics, Lecture 1 Spring 2013 5 / 22

Introduction to Statistics

Introduction to Statistics

How to treat (or analyse) data? What is random variation? Statistics is a tool for making decisions: How many computers did we sell last year? What is the expected price of a share? Is machine A more effective than machine B ? Statistics can be used Statistics can be used in most disciplines and is therefore a very important tool

Per Bruun Brockhoff (pbb@imm.dtu.dk) Introduction to Statistics, Lecture 1 Spring 2013 7 / 22 Introduction to Statistics

Statistics and Engineers

Statistics is an important tool in problem solving Data analysis Quality improvement Design of experiments Predictions of future values .. and much more!

Per Bruun Brockhoff (pbb@imm.dtu.dk) Introduction to Statistics, Lecture 1 Spring 2013 8 / 22 Introduction to Statistics

Statistics

Modern statistics Modern statistics are based

• n theory of probabilities and descriptive

statistics.

Per Bruun Brockhoff (pbb@imm.dtu.dk) Introduction to Statistics, Lecture 1 Spring 2013 9 / 22 Introduction to Statistics

Statistics

Statistics is often about analyzing a sample, that is taken from a population Based on the sample, we try to generalize (or comment on) the population Therefore it is important that the sample is representative of the population

Per Bruun Brockhoff (pbb@imm.dtu.dk) Introduction to Statistics, Lecture 1 Spring 2013 10 / 22

Descriptive Statistics: Summary Statistics

Chapter 2: Summary statistics

We use a number of summary statistics to summarize and describe data (stochastic variables) Mean ¯ x Median Variance s2 Standard deviation s Percentiles

Per Bruun Brockhoff (pbb@imm.dtu.dk) Introduction to Statistics, Lecture 1 Spring 2013 12 / 22 Descriptive Statistics: Summary Statistics

Mean

The mean value is a key number that indicates the centre of gravity or centering of the data The mean: ¯ x = 1 n

n

• i=1

xi We say that ¯ x is an estimate of the mean value

Per Bruun Brockhoff (pbb@imm.dtu.dk) Introduction to Statistics, Lecture 1 Spring 2013 13 / 22 Descriptive Statistics: Summary Statistics

Median

The median is also a key number, indicating the center of the data. In some cases, for example in the case of extreme values, the median is preferable to the mean Median: The observation in the middle (in sorted order)

Per Bruun Brockhoff (pbb@imm.dtu.dk) Introduction to Statistics, Lecture 1 Spring 2013 14 / 22 Descriptive Statistics: Summary Statistics

Variance and standard deviation

The variance (or the standard deviation) indicates the spread of the data: Variance s2 = 1 n − 1

n

• i=1

(xi − ¯ x)2 Standard deviation s = √ s2 =

• 1

n − 1

n

• i=1

(xi − ¯ x)2

Per Bruun Brockhoff (pbb@imm.dtu.dk) Introduction to Statistics, Lecture 1 Spring 2013 15 / 22

Descriptive Statistics: Summary Statistics

The coefficient of variation

The standard deviation and the variance are key numbers for absolute variation. If it is of interest to compare variation between different data sets, it might be a good idea to use a relative key number, the coefficient of variation: V = s ¯ x · 100

Per Bruun Brockhoff (pbb@imm.dtu.dk) Introduction to Statistics, Lecture 1 Spring 2013 16 / 22 Descriptive Statistics: Summary Statistics

Percentiles

The median it the point that divides the data into two halves. It is of course possible to find other points that divide the data in other parts, they are called percentiles. Often calculated percentiles are 0, 25, 50, 75, 100 % percentiles (quartiles) and/or 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 % percentiles Note: the 50% percentile is the median

Per Bruun Brockhoff (pbb@imm.dtu.dk) Introduction to Statistics, Lecture 1 Spring 2013 17 / 22 Descriptive Statistics: Summary Statistics

Figures/Tables

Quantitative data: Scatter plot (xy plot) Histogram Cumulative distribution Boxplots Count data: Bar charts (pareto diagram) Pie charts

Per Bruun Brockhoff (pbb@imm.dtu.dk) Introduction to Statistics, Lecture 1 Spring 2013 18 / 22 Software: R

Software: R

Appendix C in the textbook (7. and 8. edition): Description of R. R Commander: a graphical user interface. R-exercise today. You can run R from the G-bar at home via Thinlinc. R can (easily) be installed on your own

• computer. (See Rnote)

Per Bruun Brockhoff (pbb@imm.dtu.dk) Introduction to Statistics, Lecture 1 Spring 2013 20 / 22

Software: R

Next week:

Discrete distributions - chapter 4.

Per Bruun Brockhoff (pbb@imm.dtu.dk) Introduction to Statistics, Lecture 1 Spring 2013 21 / 22 Software: R

Agenda

1 Practical Information 2 Introduction to Statistics 3 Descriptive Statistics: Summary Statistics 4 Software: R

Per Bruun Brockhoff (pbb@imm.dtu.dk) Introduction to Statistics, Lecture 1 Spring 2013 22 / 22