1Notes:2Notes：3Notes:4Notes:5Notes：Descriptive and inferential are the classic ways to dividestatistics。
Descriptive statistics are used to characterize populations.Inferential statistics is a relatively new way to draw conclusions about populations by using relatively small samples of data from the population.One of the goals of Six Sigma is to derive an inferential statistical model and then translate it into a practical processmodel. This is known as y = f(x.6Notes:Data is collected not to evaluate each individual data point， but to generate statistics。
Statistics help to describe the process (or population and determine its behavior。
As a process is delivering a good or service， an analyst can dipinto the stream of output, gather a representative sample， calculate the statistics of the sample, and then infer about thepopulation defined by the total process output。
7Notes：Many questions about a process can be answered usingstatistics。
The customer is interested in receiving product thatmeets specific characteristics. The process needs to be sampled to determine how well it is performing to the customer expectations。
Statistics provides a quantitative means for examination。
8Notes:There are four important attributes to a given process that needto be determined in order to fully profile performance。
LOCATION –where the process output tends to clusterSPREAD –how much variation exists around the cluster pointSHAPE –what is the pattern of frequencyCONSISTENCY –the snapshot analysis useful for decision-making9Notes:The mean is the most common measure of location (centraltendency。
However, if the data is skewed or not symmetric， the mean can be misleading。
For symmetric distributions, the median and the mean are identical。
The median is the center value in a list of data that is sorted in rank order。
For an odd number of data points， the median is the middle value in the list。
For an even number of data points，the median is the average of the two middle data points.The mode is the the value that occurs with the most frequency in the sample. The mode is most often used as a measure of the most popular option in an opinion poll.10Notes：11Notes:While the range does provide a measurement of the extremevalues of a sample， it does not give information about the variability of the data about the mean.Variance and Standard Deviation provide information about the collection of samples and how they relate to the sample mean.12Notes：13Notes：14Notes：15Notes：Symmetrical –The process is just as likely to output a low value as a high valueSkewed –Values tend to cluster at one side of the meanBimodal –Could signal two overlapping processesTruncated –Could indicate that someone (or something is sorting out values over (or under a specific value。
16Notes：Box Plot gives a graphical summary of the values in a single column and helps you identify extreme values. The default boxplot display consists of a rectangular box, representing roughly the middle 50% (interquartilerange or IQ Range of the data, and lines (or ”whiskers” extending to either side, indicating the general extent of the data。
Minitab marks the median value inside the box. Minitab also marks outliers。
A boxplot can also can depict a confidence interval （CI for the population median.17Notes:18Notes:19Notes：20Notes:P—È (p-value • p—valueªv ²÷¾Ü¥í • p-value pOpbHpUo｛²— β ó© ¬ Ǿ -ô¦Ó¨Î¥ ¦ À ª¬ ÷¾ ¤ µ . Av º`± ª ²÷¾ºªÕ Ú Æ¼ • p—value pCMھƼ»¥Ë -ó©Î¥ ¨û¸ñ¤ ⺩ӗ＠¤ • §C p—value (¤p©ó 0。
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