Exam: 4 hour multiple choice. Agenda. Course Introduction to Statistics. Lecture 1: Introduction to Statistics. Per Bruun Brockhoff
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1 Course Lecture 1: Per Bruun Brockhoff DTU Informatics Building room 110 Danish Technical University 2800 Lyngby Denmark pbb@imm.dtu.dk Agenda Per Bruun Brockhoff (pbb@imm.dtu.dk), Lecture 1 Spring / 22 Per Bruun Brockhoff (pbb@imm.dtu.dk), Lecture 1 Spring / 22 Practical information Teaching module: Tuesdays 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 Homepage: imm.dtu.dk Note about software R Syllabus, Lecture plan Exercises & solutions Slides Podcasts of lectures (In English AND Danish) Quizzes Campusnet: Messages and (certain) file sharings Per Bruun Brockhoff (pbb@imm.dtu.dk), Lecture 1 Spring / 22 Per Bruun Brockhoff (pbb@imm.dtu.dk), Lecture 1 Spring / 22
2 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), Lecture 1 Spring / 22 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), Lecture 1 Spring / 22 Statistics Modern statistics Modern statistics are based on theory of probabilities and descriptive 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), Lecture 1 Spring / 22 Per Bruun Brockhoff (pbb@imm.dtu.dk), Lecture 1 Spring / 22
3 Chapter 2: Summary statistics Mean We use a number of summary statistics to summarize and describe data (stochastic variables) Mean Median x Variance s 2 Standard deviation Percentiles s The mean value is a key number that indicates the centre of gravity or centering of the data The mean: x = 1 n n We say that x is an estimate of the mean value x i Per Bruun Brockhoff (pbb@imm.dtu.dk), Lecture 1 Spring / 22 Per Bruun Brockhoff (pbb@imm.dtu.dk), Lecture 1 Spring / 22 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) Variance and standard deviation The variance (or the standard deviation) indicates the spread of the data: Variance s 2 = 1 n (x i x) 2 n 1 Standard deviation s = s 2 = 1 n 1 n (x i x) 2 Per Bruun Brockhoff (pbb@imm.dtu.dk), Lecture 1 Spring / 22 Per Bruun Brockhoff (pbb@imm.dtu.dk), Lecture 1 Spring / 22
4 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 = 100 s x Per Bruun Brockhoff (pbb@imm.dtu.dk), Lecture 1 Spring / 22 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 Per Bruun Brockhoff (pbb@imm.dtu.dk), Lecture 1 Spring / 22 Note: the 50% percentile is the median 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), Lecture 1 Spring / 22 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), Lecture 1 Spring / 22
5 Next week: Agenda 1 Discrete distributions - chapter Per Bruun Brockhoff (pbb@imm.dtu.dk), Lecture 1 Spring / 22 Per Bruun Brockhoff (pbb@imm.dtu.dk), Lecture 1 Spring / 22
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