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LESSON PURPOSE: To master the basics of variation statistics, the skills of calculating and assessing the reliability of average values

LESSON METHODOLOGY: Students independently prepare for a practical lesson in the recommended literature and complete their individual homework. The teacher within 10 minutes checks the correctness of homework and indicates the mistakes made, checks the degree of preparation using testing and an oral survey. Then students independently calculate the average values ​​and evaluate their reliability. At the end of the lesson, the teacher checks the students' independent work.


1. What is a variation series, what types of variation series are distinguished in statistics, what are the elements of a variation series.

2. What are the average values, the possibilities of their use in medicine and the practice of a doctor.

3. Types of average values: mode, median, arithmetic mean

4. The method of calculating the arithmetic mean and parameters characterizing the average.

5. What mathematical laws make it possible to theoretically substantiate the reliability of statistical data.

6. How to determine the average error of the average value.

7. What is meant by the confidence boundary of derived quantities.

8. Assessment of the reliability of differences in average values ​​using a confidence coefficient t.

9. Assessment of the reliability criterion for large and small samples.


In medical and social research, along with absolute and relative, averages are widely used. The average value is the aggregate generalizing characteristic of quantitative characteristics, it is usually indicated by the letter M or X. The average values ​​differ significantly from the statistical coefficients:

1. Coefficients characterize a sign that occurs only in some part of the statistical team, the so-called alternative sign, which may or may not occur (birth, death, illness, disability).

The average values ​​cover the signs inherent in all members of the team, but to a different extent (weight, height, treatment days in the hospital).

2. Coefficients are used to measure quality attributes. Average values ​​are for varying quantitative traits.

The use of averages in medical and social research is widely used in the study of physical development. In addition, the average values ​​apply:

1. To characterize the organization of work of medical institutions and assess their activities:

a) in the clinic: indicators of the workload of doctors, attendance at the clinic, the average number of visits in the 1st year of life, the average number of children on the site, the average number of visits for a particular disease, etc .;

b) in the hospital: the average number of days a bed is spent per year; the average duration of treatment for certain diseases, etc.

c) in the bodies of sanitary and epidemiological surveillance: the average area (or cubic capacity) per 1 person, the average diet (proteins, fats, carbohydrates, vitamins, mineral salts, calories) in the daily diet of age groups in children and adults, etc.

2. To determine the physiological and physiological parameters of the body in norm and pathology in clinical and experimental studies.

3. In special demographic and medical-social studies.

To calculate the average value, it is necessary to construct a variational series - that is, a series of numerical measurements of a certain attribute, differing in magnitude.

Variation series are of the following types:

a) ranked, unranked;

b) grouped, ungrouped;

c) intermittent, continuous.

Ranked row - an ordered row; options are arranged sequentially in increasing or decreasing numerical values.

Unordered row - options are randomly arranged.

Discontinuous (discrete) series - options are expressed as integer (discrete) numbers (windows in the hut).

Continuous row - options can be expressed as fractional numbers.

Ungrouped series - each value of the options corresponds to a certain number of frequencies.

Grouped series (interval) - options are combined into groups uniting them in magnitude within a certain interval.

In statistics, it is customary to distinguish the following types of average values: mode (Mo), median (Me) and arithmetic mean (M). Fashion is the value of a varying attribute, most often found in the aggregate. In the variation series, this is the variant with the highest frequency of occurrence. Usually, the mode is a fairly close value to the arithmetic mean, coincides with it with complete symmetry of the distribution. Median - a variant dividing the variation series into two equal halves. With an odd number of observations, the median is the variant with the sequence number (n + 1) in the variational series: 2. The arithmetic average value (M), unlike the mode and median, is based on all the observations made, therefore it is an important characteristic for the entire distribution.

The degree of diversity (variability) of the characteristic in the variation series can be estimated by the coefficient of variation (ratio of the standard deviation to the average value, multiplied by 100%); with a variation of less than 10%, a slight diversity is noted, with a variation of 10-20% - average, and with a variation of more than 20% - a strong diversity of the trait. If it is not possible to compare the variational series with others, then use the rule of three sigma. If one sigma is added to the average, then this calculated average corresponds to 68.3%, with two sigma - 95.4%, with three sigma - 99.7% of all signs. In medicine with a value of M ± 1? the concept of norm is connected; deviations from the average (in either direction) are greater than 1 ?, but less than 2 ?, are considered subnormal (above or below the norm), and if deviations from the average are more than 2 ?, the options are considered significantly different from the norm (pathology )

A measure of the reliability of the average indicator along with its error are the confidence limits and the reliability of the difference between the two average values.


TASK №1. Determine the fashion and median of the variation series. Based on the data presented, calculate: arithmetic mean by the method of moments, mean square deviation, coefficient of variation, arithmetic mean error

Task 1

Calculate the average length of stay in the surgical department of the hospital

Task 2

Calculate the average duration of temporary disability in hypertension stage II (hypertensive crisis)


Calculate the average heart rate in a group of healthy men aged 22 years after moderate exercise

Task 4.

Calculate the average living space per person in low-income families

Task 5.

Calculate the average weight of 12 year old girls brought up in a boarding school

Task 6.

Calculate the maximum muscle strength of the right hand in 15-year-old boys who regularly attend sports sections

Task 7.

Calculate the average height of 17-year-old girls in secondary school.

Task 8.

Calculate the average number of patients accepted by the local GP for one working day.

Task 9.

Calculate the average number of children in a Dagestan family

Task 10.

Calculate the average number of decayed teeth in 18 year old students at the Medical Academy (KPU index)

Task 11.

Calculate the average number of children in the first year of life living in one pediatric unit

Task 12.

Calculate the average number of missed classes in the discipline "Public Health and Health Care" by 4-year students of the Faculty of Medicine in the spring semester

Task 13.

Calculate the average growth of draftees in the Stavropol Territory

Task 14.

Calculate the average number of patients admitted by the surgeon in the clinic per one working day

TASK №2. For the average values ​​calculated in the previous task, determine the confidence limits with a probability of an error-free forecast of 95%.

Recommended Reading.

• Yu.P. Lisitsyn. Public health and healthcare. Textbook for high schools. M., 2002.

• Yu.P. Lisitsyn. Social hygiene (medicine) and healthcare organization. Kazan, 1999. - p. 288-289.

• VK. Yuriev, G.I. Kutsenko. Public health and healthcare. S.-P., 2000. –s. 191-199.

• A.F. Serenko, V.V. Ermakov. Social hygiene and healthcare organization. M., 1984. — pp. 124-146.

• Public health and healthcare. Ed. V.A. Minyaeva, N.I. Vishnyakova. M. "MEDpress-inform", 2002. –s. 97-107.

• Guidelines on social hygiene and healthcare. Ed. Yu.P. Lisitsyna. M., 1987.

• Zaitsev V.M., Livland V.G., Marinkin V.I. Applied Medical Statistics. S.-P. The Tome, 2003.
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