2WS30_partI.pdf

# Francisco were monitored between 1960 and 1967 and

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certain health cooperative (in S. Francisco) were monitored between 1960 and 1967 and figures like the mothers age, smoking status, baby weight at birth, etc… were collected (a total of 1236 valid entries) For instance, this is a list of the mother s age (in years) 27 33 28 36 23 25 33 23 25 30 27 32 23 36 30 38 25 33 33 43 22 27 25 30 23 27 ( ) We desire to make meaningful statements about mothers in S. Francisco, but using only this sample…

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I.16 Descriptive Statistics Typically we can only say something sensible about data or a dataset if we assume a statistical model for it. Nevertheless, a good start is to summarize the contents of a dataset , or represent them in a palatable way. This is also a key aspect of Exploratory Data Analysis. This is the goal of Descriptive Statistics , which are either numerical or graphical summaries and representations of data. In what follows we will concentrate mostly on scenarios where the ordering of the elements in the dataset is not considered important. E.g.: • Exam grades of 2WS30 • Customer satisfaction ratings of a store • Number of rotten apples in each crate of apples from a certain producer (order of the crates doesn t matter)
I.17 A Typical Dataset Population (mothers in S. Francisco) Sample (a small number of mothers in S. Francisco) Our hope is that the sample is somewhat representative of the entire population… Before trying to do this, let s see if we can understand the data a bit better, and summarize it in nice ways…

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I.18 Definition: Sample Mean/Sample Average Often it is good to have an idea of where the data values are hovering around. There are a number of natural ways to quantify this: For the dataset of the previous slides we have Numerical Summaries – Sample Mean Clearly this is good information to have, but it would be good to know if mother s age is always close to this, or differs wildly…
I.19 Sample Variance/Standard Deviation Definition: Sample Variance/Standard Deviation In our example Notice the units are squared !!! The sample standard deviation is given by A intuitive interpretation of what the sample standard deviation represents is not so easy, but we can still understand why it does measure variability:

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I.20 Sample Variance/Standard Deviation always non-negative Properties: Sample Variance/Standard Deviation The last expression makes handmade computations typically easier, but numerically it can be a very bad choice…
I.21 The Sample Range Definition: Sample Range Another way to assess variability: In our example This seems fishy. Actually, there are two entries in the data that are 99. It turns out this value is not the age of the mother, but rather indicates their age was unknown. So we must treat these two entries as missing values. Removing these you ll get

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I.22 Other Numerical Summaries Definition: Order Statistics There are many other numerical summaries that are important (we ll encounter these again, in the context of graphical representations of data)
I.23 Sample Median and Percentiles Definition: Sample Median

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