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Statistical Concepts in Metrology_4

Tham khảo tài liệu 'statistical concepts in metrology_4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Box Plot. Customarily a batch of data is summarized by its average Simpo PDF Merge and Split Unregistered Version - http ZZwww.simpopdf.comnor-mal distribution as explained in expression 2-0 . Certain features of the data e.g. skewness and extreme values are not reflected in the average and standard deviation. The box plot due also to Tukey presents graphically a five-number summary which in many cases shows more of the original features of the batch of data then the two number summary. To construct a box plot the sample of numbers are first ordered from the smallest to the largest resulting in X 1 1 x 2 i x n Using a set of rules the median m the lower fourth Ft and the upper fourth Fu are calculated. By definition the interval Fu Ft contains half of all data points. We note that m Fu and Ft are not disturbed by outliers. The interval Fu Ft is called the fourth spread. The lower cutoff limit is F - 1-5 FU - Ft and the upper cutoff limit is Fu 1.5 FU - Ft . A box is then constructed between Ft and Fu with the median line dividing the box into two parts. Two tails from the ends of the box extend to Xịy and n respectively. If the tails exceed the cutoff limits the cutoff limits are also marked. From a box plot one can see certain prominent features of a batch of data 1. Location - the median and whether it is in the middle of the box. 2. Spread - The fourth spread 50 percent of data - lower and upper cut off limits 99.3 percent of the data will be in the interval if the distribution is normal and the data set is large . 3. Symmetry skewness - equal or different tail lengths. 4. Outlying data points - suspected outliers. 33 The 48 measurements of isotopic ratio bromine 79 81 shown in Fig. 1 Simpo PDF Merge and Split Unregistered Version - http www.simpopdf.com h. Box plots for instrument I instrument II and for both instruments are shown in Fig. 2. INSTRUMENT I INSTRUMENT II COMBINED I II Fig. 2. Box plot of isotopic ratio bromine 79 91 . The five number summary for .