- •Laboratory work №4.6
- •Automation of statistical computing
- •In Mathcad to determine the sample variance stored in the matrix X, intended the function var (X) - sample variance, and the value of d can be calculated by the formula:
- •Variance and standard deviation (two methods of calculation).
- •Picture 2.3- Solutions Example 2.2
- •2. The duration of the operation of electron tubes of the same type (the times)
- •3. Measuring the capacity of 80 field-effect transistors
- •4. Hour of recovering diodes from the same batch (nanoseconds)
- •5. The hours of reaction (in seconds):
- •6. Given a sample mass of steel billets (g).
- •7. Changes of the limits of the strength on break for the steel sheet
- •8. The depth of the diffusion layer, defined by the sample from the party of the chips, has the following values (μm)
- •9. At a given current of 10 mA was measured direct voltage drop on the diodes Obtained the following values (volts)
- •10. Measuring the mass of a substance as the result of a chemical reaction (g)
- •11. The productiveness of the Department within 20 working days was characterized by the following numbers (in conventional units)
- •12. For 24 details was obtained the following deflection of control size from the nominal value (μm)
- •13. Measured resistivity in the sample batch of chips after doping the polysilicon
- •14. Data on the average number of family members
- •15. Given the following data on the yields of wheat
- •16. Data about tariff rank of 50 workers of one of the department of the plant
- •17. The output of services by category (2010/2009%)
- •18. Interest rates on loans (collateral loan, %)
- •19. The average population growth (cm)
- •20. The importance of the results on a 10-point greatest scale
- •21. The structure of gdp(gross domestic product) in 2000 and 2010 (industry - construction)
- •22. The fact of the execution of the plan by the company by product types (th.Units)
- •23. Data about the value of fixed assets of 50 enterprises
- •24. The dynamics of power consumption 24 1990 2010 (gw.H)
- •25 Coefficient of work motivation
Laboratory work №4.6
Automation of statistical computing
The purpose of the work: formation of practical skills in determining numerical characteristics of one-dimensional samples.
In most statistical calculations we work with samples: either with random data, obtained in the course of any experiment or the results of random number generation. Consider the possibilities of MathCad calculation of numerical characteristics of random data. Mathcad has a number of built-in functions for calculations of the numerical statistical characteristics of random data series.
Primary data processing usually consists of finding the maximum and minimum values of the sample, as well as in the construction of a series of variations - array of sample values, recorded in ascending order. The minimum and maximum elements of a sample are related to indicators of the position. For these calculations are the corresponding functions max (x), min (x) - the maximum and minimum value of a sample. To built a variation series, it is used the function sort (x).
Each random variable is completely determined by its distribution function. During the solution of practical tasks, sometimes it is necessary to know several numerical parameters that allow you to present the main features of the random variable in a condensed form. These variables include primarily the mathematical expectation and variance.
The average value of the sample is calculated by the formula
n
x i
m* i1
n
To calculate in Mathcad sample mean it should be used the function mean (x).
The sample median splits the sample in half: left and right of it appears the same number of elements in the sample. If the number of elements in the sample is even, n = 2k, then the sample median is determined by the formula: (xk+x k+1)/2, xk and x k+1 – k-і і (k+1)-е are sample values of the series variations. In an odd sample size (n = 2k + 1), as the median values it is taken value x k+1 .
In Mathcad to calculate the sample median of the sample, stored in the matrix x, assigned the function median (x) - the sample median (median) – the argument value that divides the histogram of probability density into two equal parts.
The indicators of dispersion include the dispersion sample (sample variance), standard deviation, the scope of the sampling, the coefficient of kurtosis (kurtosis sampling).
The variance of a random variable characterizes the degree of decoding values of a random variable around its mathematical mean. The sample variance is called the value:
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