Stat 155, Section 2, Last Time Numerical Summaries of Data: –Center: Mean, Medial –Spread: Range, Variance, S.D., IQR 5 Number Summary & Outlier Rule Transformation & Summaries Course Organization & Website

Reading In Textbook Approximate Reading for Today’s Material: Pages Approximate Reading for Next Class: Pages ,

And now for something completely different Collect data (into Spreadsheet): Years stamped on coins (chosen denomination) Many as person has Enter into spreadsheet Look at “distribution” using histogram

And now for something completely different Unfortunately I lost the data… Didn’t save file??? Saved to Strange Location??? Anyway, I can’t find it… So won’t be able to finish this

A Special Request Professor Marron, I am having a lot of trouble creating time plots. Is there any way that you could walk me through creating one again or demonstrate on Tuesday? I read over the notes and the book but that didn't help. Thanks!

Exploratory Data Analysis 3 “Time Plots”, i.e. “Time Series: Idea: when time structure is important, plot variable as a function of time: variable time Often useful to “connect the dots”

Airline Passengers Example A look under the hood Use Chart Wizard Chart Type: Line (or could do XY) Use subtype for points & lines Use menu for first log10 Although could just type it in Drag down to repeat for whole column

Modelling Distributions Text: Section 1.3 Idea: Approximate histograms by: an “idealized curve” i.e. a “density curve” that represents the underlying population

Idealized Curve Example Recall Hidalgo Stamps Data, Shifting Bin Movie (made # modes change): Add idealized curve: Note: “population curve” shows why histogram modes appear and disappear

Interpretation of Density Areas under density curve, give “relative frequency” Proportion of data between = = Area under =

Interpretation of Density Note: Total Area under density = 1 (since relative freq. of everything is 1) HW: 1.80 (a: l = w = 1 b: 0.25 c: 0.5), 1.81, 1.83 Work with pencil and paper, not EXCEL

Most Useful Density “Normal Curve” = “Gaussian Density” Shape: “like a mound” E.g. of “sand dumped from a truck” Older, worse, description: “bell shaped”

Normal Density Example Winter Daily Maximum Temperatures in Melbourne, Australia Notes: Top Histogram is “mound shaped” Plus “small scale random variation” So model with “Normal Density”?

Normal Density Curves Note: there is a family of normal curves, indexed by: i.“Center”, i.e. Mean = ii.“Spread”, i.e. Stand. Deviation = Terminology: & are called “parameters” Greek “mu” ~ m Greek “sigma” ~ s

Family of Normal Curves Think about: “Shifts” (pans) indexed by “Scales” (zooms) indexed by Nice interactive graphical example: (note area under curve is always 1)

Normal Curve Mathematics The “normal density curve” is: usual “function” of circle constant = 3.14… natural number = 2.7…

Normal Curve Mathematics Main Ideas: Basic shape is: “Shifted to mu”: “Scaled by sigma”: Make Total Area = 1: divide by as, but never

Normal Model Fitting Idea: Choose to give: “good” fit to data. Approach: IF the distribution is “mound shaped” & outliers are negligible THEN a “good” choice of normal model is:

Normal Fitting Example Revisit Melbourne Daily Max Temps Fit curve, using “Visually good” approximation

Normal Fitting Example A look under the hood Use chosen (not default) histogram bins for nice comparison bins Use longer range to avoid the “More” bin Can compute with density formula (Two steps, in cols F and G) Or use NORMDIST function (col J, check same as col G)

Normal Curve HW C5: A study of distance runners found a mean weight of 63.1 kg, with a standard deviation of 4.8 kg. Assuming that the distribution of weights is normal, use EXCEL to draw the density curve of the weight distribution.