Picture 2.3- Solutions Example 2.2

The most obvious form of graphical representation of the samples is the histogram. The histogram is a graph, that approximates random data density distribution. During the building of histogram the range of values of random variables [a,b] is divided into several segments, and then is the calculate of the percentage of entering data in each segment. In MathCad to build the histogram are several built-in functions.

• histogram (seg, x) - histogrammy matrix consisting of column segments partitioning and column frequencies entering these intervals of histogram.

• seg - number of segments constructing histogram

• x - vector of random data.

Using this function it can built a frequency polygon - a broken line connecting the points with abscissa equal the middle of intervals group, and the ordinate equal to the corresponding frequencies.

Examples of using the histogram shown in picture.2.4

c  rnorm(1000 0 1)
				0	1
f  histogram(10 c)			0	0	1
			1	1	12
			2	2	48
			3	3	166
		f 
			4	4	300
			5	5	287
			6	6	144
			7	7	35
			8	8	7
			9	9	0

			320
			280
			240
f		1	200
			160
			120
			80																					40
			40
			0
				0		2											4				6			8
															f			0

Picture 2.4 Graph and matrix of histogram

To create a schedule in the form histogram you need:

• build a two-dimensional graph on the axes, set variables on the axes and limit x-axis;

• In the dialog window Formatting Currently Selected Graph selected graphics accessing the Traces;

• Set to the given histograms in field Type list item bar or solidbar;

• Click the OK button.

Configure Windows histohram images and graphs are presented in picture.2.5

Picture 2.5 - Windows setting histograms

Variants for individual tasks

To build a variational series. To calculate the sample characteristics:mathematical expectation, sampling variance, corrected sample variance, standard deviation, the scope of the sample, sample kurtosis. To draw a graphic representation of the sample (empirical function, the cumulative curve, histogram).

1 Hour decision control task (min.):

38		60			41		51		33			42			45			21		53	60			68	52		47
49		14			57		54		59			11			47			28		48	58			32	42		58