Francisco were monitored between 1960 and 1967 and

Info icon This preview shows pages 15–24. Sign up to view the full content.

View Full Document Right Arrow Icon
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…
Image of page 15

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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)
Image of page 16
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…
Image of page 17

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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…
Image of page 18
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:
Image of page 19

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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…
Image of page 20
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
Image of page 21

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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)
Image of page 22
I.23 Sample Median and Percentiles Definition: Sample Median
Image of page 23

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 24
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern