Textbook Notes (368,401)
Canada (161,862)
Statistics (133)
STAB22H3 (130)
Chapter 5

Chapter 5.docx

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Mahinda Samarakoon

Stats: Data and Models – Canadian Edition Chapter 5 – Understanding and Comparing Distributions Boxplot and 5-Number Summaries - 5-number summary can be displayed in a boxplot - Making the boxplot: o Vertical axis spanning the extent of the data o Indicate Q1, median, and Q3 with short horizontal lines, and connect them with vertical lines to form a box o (in class) indicate the minimum and maximum values with an asterisk (*), connect the *s to the box with a straight line o Erect “fences” around the main part of the data to identify outliers, shown with a dotted line – place the upper fence 1.5 IQRs above Q3 (Q3 + 1.5IQR) and the lower fence 1.5 IQRs below Q1 (Q1 – 1.5IQR) o If a data value falls outside the fences, it does not get connect with a whisker (the line from the box connecting the min. and max. values)  If the min. or max. value falls outside of the fence, the most extreme value within the fences is also marked (because it is the highest/lowest non-outlier) - The height of the box made by the Q1, median, and Q3 is equal to the IQR - If the median is roughly at the centre of the box, the middle half of the data is roughly symmetric, if it is not centred, the distribution is skewed - The length of the whiskers also indicate distribution symmetry/skewness Comparing Groups with Boxplots - Boxplots offer a balance of information and simplicity; hide the details while displaying the overall summary information - Looking at boxplots side-by-side, we can see which groups have higher medians, greater IQRs, and greater ranges Outliers - Cases that stand out from the rest of the data almost always deserve our attenti
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