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Lecture 1

STAT151 Lecture 1: Pre-Midterm Notes

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Alireza Simchi

Stat 151 Jan. 9, 17 Chapter 1: - Information we gather is called data - Statistics is science of how to collect, summarize, analyze, present, and interpret data o And making decisions on them - Three main aspects of stats o Design – how to obtain data – chapters 9-11 ▪ Data must represent population o Description – methods to describe data – chapters 2-8 o Inference – making decisions and predictions based on data – chapters 16-25 o Probability – chance of statistic being accurate – chapters 12-15 - Stats is using data to get knowledge about world around us o Population - entire group of objects which information is collected o Sample – part or subset of the population used to collect data o Parameter – numerical summary of population o Statistic – numerical summary of sample o Inferences – statements about population based on sample - Mean = average - 𝜇 = average of population Jan. 11, 17 - Read chapter 9-11 - Variables – a value that varies that describes a characteristic of person/thing o Numbers or labels o Distinguish the type of variable during a study o Categorical/qualitative ▪ Nominal – none is better than another ▪ Ordinal – some are better than others in specific order o Measurement/quantitative ▪ Discrete – whole number quantity ▪ Continuous – can have values between whole numbers ▪ *student ID is identifier variable - Date values need context - 5 w’s o Who what where when why Chapter 2: - Chapter 2 focuses on categorizing categorical variables - Population – everyone - Observational study – independent variable is not controlled by researcher - Experimental study – independent variable is controlled by researcher - Stratified samples select people from each group - Volunteer sample – people have strong feeling for study, and therefore gives bias a study - Lurking or confounding variables – might affect results - Cannot make casual inference in observational study* - Might be able to make casual inference to population only in randomized experiment - Frequency – count of a variable - Relative frequency – proportion of all data Jan. 13, 17 - Bar chart – for non-measurement data - Pareto diagram – bar chart largest to smallest - Segmented bar chart – one on top of another - Pie chart - Marginal/joint/conditional distribution** - Contingency table – one variable on row, other on column o Can calculate relative frequencies differently when calculating from different totals ▪ Conditional distribution Chapter 3: Displaying and summarizing quantitative data - Average = mean = 𝑥̅ = ∑𝑥 𝑛 - Mean does not represent center of data o Do not take out outliers - Median is centre of data 𝑛+1 o 2 – if answer is decimal, use intermediate of the two nearby data values - Mode is value with highest frequency o Does not exist when everything once o Mode does not need to be unique – can be more than one mode Jan. 16, 17 - If there is outlier, use median. Otherwise, use mean - Dot plot – dot on graph for every data o Not very useful - Stem and leaf display o Table-like with second digit on left and multiple first digits on the right - Histogram o Good for summarizing lots of data - Density – area = relative frequency - Numbers of humps o Uniform – 0 o Unimodal o Bimodal o Multimodal - Right/left positive/negative skewed distribution - Centre – the value(s) that splits data in half o In a skewed distribution use median - Spread o The range of values , concentration, or the most of values around centre – range, standard deviation, IQR th th - p percentile is a number so tha
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