STAT 210 1st EditionLecture 10Outline of Last LectureI. Measures of Central LocationII. RangeOutline of Current LectureIII. Measures of Central Location (cont.)IV. BoxplotsCurrent LectureV. Mean – influenced by outliersa. Population mean denoted by b. Sample mean denoted by x barVI. Median – resistant to outliersa. Population median denoted by b. Sample median denoted by MVII. Range – measure of overall spread, influenced by outliersVIII. Standard deviation – measure of spread around the mean, influenced by outliersa. Population standard deviation denoted by b. Sample standard deviation denotes s IX. Interquartile Range – measure of spread around the median, resistant to outliersX. Boxplots – a graphical display which uses several of the numerical measures to give information on the symmetry of shape of the distribution, the central location and variability (spread) in a distribution and on the concentration of scores in tails of distribution (outliers) a. Order the data from smallest to largestb. Compute a five number summaryi. Minimum Q1 Median Q3 Maximumc. Interquartile Range: IQR = Q3 – Q1d. Lower fence = Q1 – 1.5(IQR)e. Upper fence = Q3 + 1.5(IQR)f. Any observation less than the lower fence value or greater than the upperfence value is an outlierg. After removing the outliers, the lower adjacent value is the smallest observation that remains in the data set and the upper adjacent value is the largest observation that remains in the data seth. Draw boxploti. Draw and label an axis.ii. Construct a box, where the ends of the box are Q1 and Q3iii. Draw a line through the box corresponding to the medianiv. Mark an “x” at the lower and upper adjacent values, and draw a dashed line from each “x” to the end of the box.XI. Boxplots in generala. Location of center (median)b. Measure of spread (interquartile range or range)c. Shape (symmetry or skewness)d. Existence of outliersXII. Ideal boxplot is symmetric with no outliers XIII. A symmetric boxplot with long whisker or several outliers at each end indicate that the data may come from a distribution with long tails; occasionally called long-tailed distributionsXIV. A skewed boxplot or a boxplot with several outliers indicates that the data is either from a skewed distribution or a distribution with long tails. A boxplot is skewed if the median is not in the center of the box or if one of the adjacent values is closer to the box than the other.XV. Side-by-side boxplots can be constructed and used to compare the distributions of several distributions. To create side-by-side boxplots, label one axis and draw several boxes next to