STAT 2004, Week 4: Boxplots, Robust Statistics
STAT 2004, Week 4: Boxplots, Robust Statistics STAT 2004
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This 2 page Class Notes was uploaded by Mara DePena on Saturday February 13, 2016. The Class Notes belongs to STAT 2004 at Virginia Polytechnic Institute and State University taught by Metzger in Spring 2016. Since its upload, it has received 58 views. For similar materials see Introductory Statistics in Statistics at Virginia Polytechnic Institute and State University.
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Date Created: 02/13/16
STAT 2004 CHAPTER ONE: WEEK 4 SAMPLE STATISTICS n 2 1 2 Sample variance- s = n−1 i=1x ix´) Sample standard deviation- Tells you how spread out your data is. It is the square root of the variance. QUANTILES Also known as percentiles. o If you are in the 70 percentile, you are better than 70% of your class and not as good as 30%. DISTRIBUTION Describes shape, center, and spread/variation of data. For the images below, imagine histograms that fit the depicted curves. BOXPLOT A boxplot uses a five number summary consisting of the median (Q ), 2 minimum, maximum, and 25 (Q ) and 75 (Q ) percentile. It 1 3 summarizes a data set while also plotting unusual observations known as outliers. o Outliers- Observations that are extreme relative to the rest of the data. Below is an example of a boxplot depicting test scores. Boxplots are usually vertical, but this one will be depicted horizontally. o The first step is to draw the median. The second step is to draw a rectangle to represent the middle 50% of the data. Interquartile range (IQR)- Q3-Q1. It is the length of the box in the boxplot. IQR Method o One of the many methods for calculating outliers. Lower cutoff- Q 1 (1.5 x IQR) Upper cutoff- Q 3 (1.5 x IQR) These upper and lower cutoffs make the whiskers attached to the box. Any points outside of the whisker range are considered outliers and are labeled with a dot. A Cauchy histogram has outliers. ROBUST STATISTICS Robust estimate- Strong/effective in all/most situations and conditions. Outliers do not change it very much. The median and IQR are considered robust estimates. SYMBOL KEY x Median ´ Mean Population mean ❑ Estimation 2 Variance Standard deviation
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