3.3 continued Review of last lecture where we left off:Computing the Median The median is the measure of center To compute the median sort the values from small to largeo For even numbers take the average of the two middle most numberso For odd numbers take the center valueStart Lecture 4, finishing up chapter 3Quartiles Quartiles help s locate measure in data Q1 is at a value where 25% of the data lies at or below Q1. o Q1 Is the median of the lower half Q3 is at a value where 75% of the data lies at or below Q3o Q3 is the median of the upper half  Q2 is the median of the entire distribution 50% of the data lies on either side of it. The Interquartile range or the IQR The interquartile range represents the middle range of 50% To find the interquartile range divide the data in to four equal parts the two innermost parts are the interquartile range. o Q3-Q1=IQRThe Range The range is the distance of the whole data seto The range is equal to the maximum value subtracted from the minimum value The range is sensitive to outliers The range of a small sample is not representative of the entire populationChapter 4:Numerical Summaries Part 2 Short review:  The mean is all the values in a data set divided by the total number of valueso on right and left skewed distribution the mean falls respectively to the right or the left ofthe medianDescribing distributions The mean and standard deviation should be used when the distribution is mound shaped and symmetric The median and IQR should be used when the distribution is skewed right ot left  If the distribution is not unimodal, split the data by its respective modes.Outliers Outliers are sometimes the result of an error or clerical mistake In a small sample the mean is strongly effected by outliers  The mean, standard deviation, and the range are all affected by outliers  The median and the interquartile range or the IQR are both not affected by outliers Bimodial Distributions  The mean and median don’t represent typical value for most bimodial distributions If there are two separate sub groups they need to be individually represented with graphs and statisticsProblem with bimodal distributions  There are two typical values  The mean and the median are not representative of typical valueso We need to separate/split up the groups Separating Bimodal Distributions By separating distribution data in to two histograms allow them to be compaired o By doing this we can compare mean to mean and median to median 5 Point Summary When data is divided in to 4 equal segments, 5 numbers repetedly arise. These 5 numbers are known as a 5 point summary.o The minimum( the smallest value)o The first quartile(the median of the lower half)o The median(the middle or center number)o The 3rd quartile(median of the upper half)o Maximum (the largest value)Potential Outliers  A potential outlier is any value that is more than 1.5 interquartile ranges below the first quartile or above the 3rd quartile o First calculate the IQR ( Q3-Q1)o Then find the m (Q1-(1.5)(IQR))o Then find M (Q3+ 1.5(IQR)) Any value less than M is a potential outlierBox Plots A box plot is a chart that visually displays Q1, Q3, the median, and outliers Box plots reveal the typical range of values, possible outliers, and variation.  Boxplots don’t reveal mode, mean, or anything for small datasets  Box plots are used to compare numerical variables against variables with a limited number of values  Box plots are more interesting when there are more than one to compare against one