2Numerical SummariesMeanMedianModeDescribing Data NumericallyVarianceStandard DeviationRangeInterquartile RangeCentral TendencyVariation
3Central TendencyMeanMedianModenxxn1ii!==Midpoint ofranked valuesMost frequentlyobserved valueArithmeticaverageMeasures of center: Mode, Median, Mean
4Measures of Center: Mode•A measure of central tendency•Value that occurs most often•Not affected by extreme values•Used for either numerical or categorical data•There may be no mode•There may be several modes0 1 2 3 4 5 6 7 8 9 10 11 12 13 14Mode = 90 1 2 3 4 5 6No Mode
5•In an ordered list, the median is the “middle”number (50% above, 50% below)•Not affected by extreme values0 1 2 3 4 5 6 7 8 9 10Median = 30 1 2 3 4 5 6 7 8 9 10Median = 3Measures of Center: Median
6Measures of Center: MedianThe Median the point that divides a distribution in half: 50% ofthe data on the left of the median and the other 50% - on theright.To find the median, arrange the data in ascending (descending) order.•If n is odd, the median is the observation with position•If n is even, the median is the average of the middle two values withthe positionsn12+nnand122+
9Boxplotis a visual representation of thefive number summary.There are four steps to built a boxplot:1. Interquartile range IQR= Q3 – Q1, shows the spread of the middle 50% of the data2. Fences•lower fence LF = Q1 – 1.5(IQR)•upper fence UF = Q3 + 1.5(IQR)3. Whiskers - extend from Q1 and Q3 to the smallest and largest observations withinthe fences4. outliers (if any) - extreme observations that fall outside the fences
10Boxplot: gas mileage for two-seater cars051015202530Collection 1Box Plot