For example: mean(data1) ans = sum(data1)/length(data1) ans = mean(data2) ans = median(data1) ans = median(data2) ans = These results can be confirmed by observing the plots of the data in Figure , in which the data values can be seen to be centered on . For the two data sets considered, the values of the mean and median are very close. This is not necessarily the case for other data sets. Also note that the results above show that mean(data1) = sum(data1)/length(data1). Measures of variation Measures of variation: indicate the degree of. | For example mean datal ans sum data1 length data1 ans mean data2 ans median data1 ans median data2 ans These results can be confirmed by observing the plots of the data in Figure in which the data values can be seen to be centered on . For the two data sets considered the values of the mean and median are very close. This is not necessarily the case for other data sets. Also note that the results above show that mean data1 sum data1 length data1 . Measures of variation Measures of variation indicate the degree of deviation of random samples from the measure of central tendency. Referring again to the plots of our random data sets data1 and data2 in Figure observe that data2 has greater variation from the mean. The sample standard deviation of vector x having N elements is s 1 1 N 1 2 1 Z x n -x 2 n 1 The sample variance s2 is the square of the standard deviation. std x Returns the sample standard deviation of the elements of the vector x. Returns a row vector of the sample standard deviations of the columns of matrix x. For example std data1 147 ans std data2 ans Thus the variation of data2 is greater than that of datal as we concluded from observation of the plotted data values. Random Number Generation Many engineering problems require the use of random numbers in the development of a solution. In some cases the random numbers are used to develop a simulation of a complex problem. The simulation can be tested over and over to analyze the results with each test representing a repetition of the experiment. Random numbers also used to represent noise sequences such as those heard on a radio. Uniform Random Numbers Random numbers are characterized by their frequency distributions. Uniform random numbers have a constant or uniform distribution over their range between minimum and maximum values. The rand function in Matlab generates uniform random numbers distributed over the interval 0 1 . A state vector
