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Unformatted text preview: Week 1: Summary Statistics and Box Plots ChE, BioE, EnvE 213
Prof. Milo Koretsky I. Measures of Central Tendency A. Mean ( x ). Measure of location or central tendency. Arithmetic mean is obtained by adding up all the samples and dividing by the number of samples: ! xi
Also called the average. B. Median. Measure of location or central tendency. Middle value in a set of data which is arranged by value. If there is an even number of samples, the median is the average of the two middle ones. C. Mode. Observation that occurs most frequently in a set of data. There may be more than one mode in a frequency distribution, e.g., bimodal. II. Measures of Dispersion Standard Deviation of the sample (s). A descriptor of the dispersion or variation within a sample. Mathematically it is the square root of the average squared deviation of the data about the mean. " ( xi ! x ) s=
i 2 n !1 Range (R). A descriptor of the dispersion or variation within a sample. Difference between the largest (in value) and smallest member of the data set: R = x max ! xm i n
III. Box Plots Box plots are useful graphical devices to compare and display sample statistical data. There are many forms that a box plot takes. On the next page is an example of a box plot for measured oxide thickness. 0.510 Thic kness µm 0.508 upper decile or maximum value 0.504 0.506 upper quartile median lower quartile lower decile or minimum value Exercise: 1. The following set of 18 readings was taken from a pressure gauge. Readings are in PSI. Construct a box plot. (100 ,120, 50, 100, 45, 26, 200, 300, 100, 150, 200, 100, 100, 100, 250, 300, 180, 100) IV. Population vs. Sample Population. Collection of all similar items about which we want to make a decision. Sample. The portion of a population or process that we actually measure. The smallest sample size is 1, the largest sample consists of the entire population (100% sample). Random Sample. A sample selected from a population in which every sample had an equal chance of being selected. Usually we try to obtain random samples. Population Mean Standard deviation µ σ Sample 0.500 0.502 x
s ! ...
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This note was uploaded on 04/17/2010 for the course CHE 213 taught by Professor Staff during the Winter '08 term at Oregon State.
- Winter '08