六西格玛6sigma基础统计学.ppt

File Normality testing.mtw Normal is Data 1 and bi-modal is data 8 If a histogram shows multiple humps (bimodal or multimodal.), the normal probability plot will show multiple sloped line segments attached with flat line segments. In order to analyse the process, we will have to segment or stratify the data and test the different underlying distributions for normality. Basic Statistics – Probability plot and normality The importance of data Types of data Representing data Statistical parameters The normal distribution Probability plot and normality Sampling The 3 graphs come from the same file (Normality Testing.mtw) The left one is column data 3, the middle one is data 9 and the right is column 10. The spread is what GE and others call SPAN These distributions are all non-normal. Central tendency: In the case of non-normal data (skewed or long-tailed distributions) it is better to use the median (Q2) as an indicator of central tendency, rather than the mean. Remember that the Median is the middle of the data set – 50% of the data is greater than the median and 50% of the data is less than the median. Variation: In the case of non-normal data instead of using standard deviation to indicate spread we typically use: P95-P5 to indicate the amount of variation in a long-tailed distribution. It is the distance between the two extremes of the data set. We typically use P95 and P5 since we don’t want this distance to be determined by one or two ‘outliers’. If we have a lot of data ( 5000 points), we often use P99-P1 to measure spread. NOTE: P5-P95 is sometimes called SPAN. Basic Statistics – Probability plot and normality The importance of data Types of data Representing data Statistical parameters The normal distribution Probability plot and normality Sampling Basic Statistics – Representing Data The importance of data Types of data Representing data – Time Series Plots – Dot Plots – Histograms and Frequency Distributions Statistical parameters The normal