Measuring Variation 2 Lecture 17 Sec 5 3 3 Mon Feb 14 2005 The Five Number Summary Five number summary A summary of a sample or population consisting of the five numbers Minimum First quartile Q1 Median Third quartile Q3 Maximum This does a better job of measuring spread than any single number can do TI 83 Five Number Summary Use the TI 83 to find a five number summary of the age data Min 32 Q1 41 Median 43 5 Q3 46 5 Max 51 The Five Number Summary From the 5 number summary of the age data can we detect skewness in the distribution Answer Maybe Boxplots Boxplot A graphical display of a fivenumber summary Draw and label a scale representing the variable Draw a box over the scale with its left and right ends at Q1 and Q3 Draw a vertical line through the box at the median Draw a left tail whisker from the box to the minimum Draw a right tail from the box to the maximum Example Draw a boxplot of the age data Boxplots and Shape What would a boxplot for a uniform distribution look like What would a boxplot for a symmetric distribution look like What would a boxplot for a leftskewed distribution look like TI 83 Boxplots Press STAT PLOT Select Plot1 Turn Plot 1 On Select the Boxplot Type Specify list L1 Press WINDOW Set minX and maxX appropriately Press GRAPH See the instructions on p 283 TI 83 Boxplots Press TRACE Use the arrow keys to see the values of the minimum Q1 the median Q3 and the maximum Modified Boxplots Modified boxplot A boxplot in which the outliers are indicated Modified Boxplots Draw the box part of the boxplot as usual Compute STEP 1 5 IQR The inner fences are at Q1 STEP and Q3 STEP Extend the whiskers from the box to the smallest and largest values that are within the inner fences Draw as individual dots any values that are outside the inner fences These dots represent outliers Example DePaul University For an example of modified boxplots see DePaul University s web page on retention Example Draw a modified boxplot of the age data Do the age data have any outliers See Example 5 6 p 286 TI 83 Modified Boxplots Follow the same steps as for a regular boxplot but for the Type select the modified boxplot icon the first icon in the second row It looks like a boxplot with a couple of extra dots Use the TI 83 to find a modified boxplot of the age data Let s Do It Let s do it 5 9 p 286 Five number Summary and Outliers Let s do it 5 10 p 287 Cost of Running Shoes Let s do it 5 11 p 288 Comparing Ages Antibiotic Study
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