Descriptive Statistics∶ Numerical Methods.ppt

Empirical Rule For data having a bell-shaped distribution: Approximately 95% of the data values will be within two standard deviations of the mean. Empirical Rule For data having a bell-shaped distribution: Almost all (99.7%) of the items will be within three standard deviations of the mean. Example: Apartment Rents Empirical Rule Interval % in Interval Within +/- 1s 436.06 to 545.54 48/70 = 69% Within +/- 2s 381.32 to 600.28 68/70 = 97% Within +/- 3s 326.58 to 655.02 70/70 = 100% Detecting Outliers（异常值的检测） An outlier is an unusually small or unusually large value in a data set. 异常值：数值异常大或数值异常小的观测值 A data value with a z-score less than -3 or greater than +3 might be considered an outlier. Interpretation: 1) It might be an incorrectly recorded data value. 2) It might be a data value that was incorrectly included in the data set. 3) It might be a correctly recorded data value that belongs in the data set. Example: Apartment Rents Detecting Outliers The most extreme z-scores are -1.20 and 2.27. Using |z| 3 as the criterion for an outlier, there are no outliers in this data set. Z-score Values for Apartment Rents 3.4 Exploratory Data Analysis Five-Number Summary Box Plot Five-Number Summary五数概括法 Smallest Value First Quartile Median Third Quartile Largest Value Example: Apartment Rents Five-Number Summary Lowest Value = 425 First Quartile = 445 Median = 475 Third Quartile = 525 Largest Value = 615 Box Plot箱形图 A box is drawn with its ends located at the first and third quartiles. A vertical line is drawn in the box at the location of the median. Limits are located (not drawn) using the interquartile range (IQR). The lower limit is located 1.5(IQR) below Q1. The upper limit is located 1.5(IQR) above Q3. Data outside these limits are considered outliers. Dashed lines are drawn from the ends of the box to the smallest and largest data values inside the limits.