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03 Stats, Histograms, Probability Distribution, Symbolic Forms.pdf

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University of California - Irvine
Douglas Tobias

Elementary statistical analysis Statistical analysis of data is ubiquitous in the physical, biological, and social sciences. There are a large number of statistical quantities that are useful for characterizing sets of data. Below we introduce the use of Mathematica to calculate several basic statistical parameters and to depict the distribution of data. We begin with a list of data that represents a set of measurements of some quantity: In[1]:=data = 81.05, 1.01, 0.97, 1.14, 0.92, 0.99, 1.07< Out[1]=81.05, 1.01, 0.97, 1.14, 0.92, 0.99, 1.07< Min and Max report the minimum and maximum values found in the list: In[2]:[email protected] Out[2]=0.92 In[3]:[email protected] Out[3]=1.14 Total sums the values in the list: In[4]:[email protected] 7.15 Out[4]= N Mean gives the mean or average value, defined as = ⁄ i=1xi, where the x ire the values in the list, and N is the number of values in the list: In[5]:[email protected] Out[5]=1.02143 Median is the central value in the list, which is evident when the values are sorted: In[6]:[email protected] Out[6]=1.01 [email protected] In[7]:= Out[7]=80.92, 0.97, 0.99, 1.01, 1.05, 1.07, 1.14< The variance, denoted s , is a measure of the spread of the values about the mean. It is defined as s = ⁄ N Hx - < x >L /(N | 1), and computed in Mathematica using the Variance command: i=1 i In[8]:[email protected] Out[8]=0.00521429 The standard deviation, s, computed in Mathematica using the StandardDeviation command, is the square root of the variance: 2 mathematica_lesson4.nb In[9]:[email protected] 0.07221 Out[9]= In[10]:=* [email protected],[email protected]@5,1DD
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