1. Accomplished by: Usmanova g.
Sampling Method
Accomplished by: Usmanova g.

2. Outline: The tasks of Mathematical Statistics
General and selective aggregate
Statistical sampling distribution. Polygon and histogram
Empirical distribution function

3. The tasks of Mathematical Statistics
Mathematical statistics - is a branch of applied mathematics, directly adjacent to the theory of probability. The main difference between mathematical statistics from the theory of probability is that in mathematical statistics observed not actions on the laws of distribution and numerical characteristics of random variables, but approximate methods for finding those laws and numerical characteristics of the results of experiments. Development of methods of recording, describing and analyzing the statistics of experimental data derived from the observations of mass random phenomena, is the subject of a special science - mathematical statistics.

4. General and selective aggregate
In mathematical statistics, studying the random variable is associated with the accomplishment of a number of independent experiments in which it takes the certain values. The resulting values of the random variable is a statistical aggregate or statistical series.
Statistical aggregate - a set of objects that are homogeneous with respect to a qualitative and quantitative features that characterize these objects.
Example: A series of tablets of the drug, standardization of tablets may serve as a good sign, and a quantitative controlled tablet weight.

5. General and selective aggregate
The aggregate consisting of all the objects that can be assigned to it, called the general.
Example: If it would be possible to study all the patients with rheumatism on the globe, then this group of patients would have been the general population. In practice, the general population is often seen in the specific range (for example, the population of specific city, a series of solutions in ampoules for injection.)
Many objects, randomly selected from the general population, called a aggregate sample or sample. The number of samples of objects called its volume.
Example: For quality control solutions in ampoules for injections on the lack of mechanical impurities, 150 ampoules are collected from the 5000 series of ampoules. Here, the amount of the general aggregate, the amount of the sample aggregate.

6. General and selective aggregate
In order the properties of aggregate sample reflect the properties of the population well enough, the sample should be representative.
Repeated sampling and unrepeated sampling

7. Statistical sampling distribution. Polygon and histogram

8. Statistical sampling distribution. Polygon and histogram
Discrete distribution series.
Example: As a result of individual tests of the activity of tetracycline hydrochloride, these values were obtained (in U / mg): 925, 940, 760, 905, 995, 965, 940, 925, 940, 905. Create a distribution series. X
760
905
925
940
965
995 m 1 2 3
P = m/n
0,1
0,2
0,3

9. Statistical sampling distribution. Polygon and histogram
Interval distribution series
Practice has shown that in most cases choice of the number of partial intervals is rational, depending on the volume of n samples using the following table.
Sample volume n
25-40
40-60
60-100
>200
The number of intervals
5-6
6-8
7-10
8-12
10-15

10. Statistical sampling distribution. Polygon and histogram
Polygons and histograms are built for a graphic representation of the statistical distribution.

11. Empirical distribution function
The empirical distribution function (sample distribution function) is called the function F * (x), which determines for each value of x the relative frequency of the event X < x:
F * (x) = m (x) / n,
where m (x) - the number of observations in which the sign of X is less than x; n - sample volume.

12. Empirical distribution function
In contrast to the empirical distribution function of the sample, the distribution function F (x) of the total population is called the theoretical distribution function.
The difference between these functions is that the theoretical function F (x) determines the probability of the event X < x, and F * (x) - the relative frequency of the event.

13. Empirical distribution function
The function F * (x) has all the properties of the function F (x):
The values of empirical functions belong to the interval [0,1].
F * (x) - a non-decreasing function.
If x1 - the smallest version, the F * (x) = 0 for x <= x1; if xk - the largest variant, the F * (x) = 1 if x> xk.

14. Empirical distribution functionxi 2 4 5 6 7 mi 3