"Random Sampling" statistics PPT courseware (stratified random sampling, ways to obtain data)

"Random Sampling" statistics PPT courseware (stratified random sampling, ways to obtain data)

Part One: Content Standards

1. Through examples, understand the characteristics and scope of application of stratified random sampling.

2. Understand the necessity of stratified random sampling.

3. Master the method of proportional allocation of sample size in each stratum.

4. Combined with specific examples, master the sample mean and sample variance of stratified random sampling.

5. Know the basic ways to obtain data, including: statistical reports and yearbooks, social surveys, experimental designs, censuses and spot checks, the Internet, etc.

Random Sampling PPT, Part 2 Content: Before Class • Independent Exploration

[Textbook Extraction]

Knowledge point 1: Stratified random sampling

Preview the teaching materials and think about the questions

The core issue in sample surveys is the representativeness of the sample. Simple random sampling allows every individual in the population to have an equal chance of being selected, but due to the randomness of sampling, relatively "extreme" samples may appear. For example, in a survey on the height of first-year students in Shuren Middle School, it may appear that most of the 50 individuals in the sample are tall or short. The average of this "extreme" sample will deviate significantly from the overall average, causing a large error in the estimation.

Can the sampling method be improved using some additional information from the population?

[ Tips As a sample of the population. Since corresponding individuals are selected from both groups of boys and girls, "extreme" samples can be effectively avoided. In other words, stratified sampling is required.

Knowledge point 2: Sample mean and population mean of stratified random sampling

Preview the teaching materials and think about the questions

In stratified sampling, the number of random checks in each stratum is different. How to find the average number of samples?

Knowledge sorting In stratified random sampling, if the number of layers is 2, the number of individuals included in layer 1 and layer 2 are M and N respectively, and the sample sizes extracted are m and n respectively. Use X1, X2,..., XM represents the variable value of each individual in the first layer, x1, x2,...,xm represents the variable value of each individual in the first layer sample; Y1, Y2,..., YN represents the variable value of each individual in the second layer, and y1, y2, ..., yn represent the variable values ​​of each individual in the second layer sample, then the overall mean X and sample mean x in the first layer are X-=1Mi=1MXi, x=1mi=1mxi. The overall mean Y and sample mean x of the layer are Y-=1Ni=1NYi, y-=1ni=1nyi respectively.

Knowledge point 3: Some basic ways to obtain data

Preview the teaching materials and think about the questions

Statistics is about understanding unknown phenomena through collecting data and analyzing data. Therefore, how to collect data is an important part of statistical research.

Discuss what are the main ways to obtain data?

[Autonomous detection]

1. There are 500 boys and 400 girls in the third grade of a school. In order to understand the health status of students in this year, 25 boys and 20 girls were randomly selected for investigation. This sampling method is ()

A． Simple random sampling method B. Drawing lots

C． Random number method D. stratified random sampling

Random Sampling PPT, Part 3: Classroom • Interactive Inquiry

Explore the concept of stratified random sampling

[Example 1] Among the following questions, which one is most suitable to use stratified random sampling to select samples is ()

A． Select 3 students from 10 students to participate in the symposium

B. There are 500 families in a community, including 125 high-income families, 280 middle-income families, and 95 low-income families. In order to understand a certain indicator of purchasing power, a sample with a capacity of 100 should be drawn from them.

C． From 1,000 workers, 100 were selected to investigate the time spent commuting to work.

D． There are 20 very large sales points in a certain area, and 7 of them should be selected to investigate their sales revenue and after-sales service.

method promotion

The premise of stratified random sampling and the two principles to be followed

(1) Premise: The premise of using stratified random sampling is that the population can be stratified, with large differences between strata and small differences among individuals within strata.

(2)Two principles to follow

① Divide the population into several sub-populations according to one or more variables, and each individual belongs to and belongs to only one sub-population, that is, following the principle of no duplication and no omission;

② Carry out simple random sampling independently in each sub-population, that is, follow the principle of equal probability sampling in each stratum.

1. There are four breeding rooms in a college, with 18, 54, 24, and 48 white mice respectively for testing. A certain test requires 24 white mice to be sampled. What do you think is the most appropriate sampling method? ()

A． Select 6 animals from each breeding room

B. Add collars with different numbers to all the white rats, and use random sampling to identify 24 rats.

C． Randomly select 3, 9, 4, and 8 animals from the four breeding rooms.

D． It is first determined that 3, 9, 4, and 8 animals should be selected from these four breeding rooms. Then each breeding room will add numbered collars and use simple random sampling to determine the objects to be selected.

Study 2: Sample mean and population mean in stratified random sampling

[Example 2] There are 600 residents in a certain area, including 450 ordinary families and 150 high-income families. In order to investigate the monthly consumption expenditure on dairy products of residents in the area, it was decided to adopt the stratified random sampling method and stratify according to ordinary families and high-income families. The average monthly consumption expenditure on dairy products for ordinary families and high-income families was obtained as 40 yuan and 40 yuan respectively. 90 yuan.

(1) If the samples are distributed proportionally among each stratum and the total sample size is 60, how many households are sampled from ordinary families and high-income families? In this case, please estimate the average monthly consumption expenditure on dairy products for all residents in the area.

(2) If the sample sizes drawn from ordinary households and high-income households are 30 and 30 respectively, then in this case, what is the average monthly consumption expenditure on dairy products of the 60 households sampled? Is it reasonable to use the average monthly consumption expenditure on dairy products of these 60 households to estimate the average monthly consumption expenditure on dairy products of all residents in the area? If it is unreasonable, how can we estimate it more reasonably?

Random Sampling PPT, Part 4: After Class • Quality Development

1. Obvious differences and non-intersection - the outstanding characteristics of stratified random sampling

Mathematical modeling, data analysis, mathematical operations

When the population is composed of several parts that are obviously different and do not overlap with each other, stratified random sampling is often used. When applying stratified sampling, the following requirements should be followed:

① When the overall individual differences are obvious, stratified random sampling is used.

② When stratifying, similar individuals are classified into one category, which is one layer. Stratification requires that individuals in each layer do not intersect with each other, that is, follow the principles of no duplication and no omission, that is, ensure the consistency of the sample structure and the overall structure.

③ Stratified random sampling In order to ensure that each individual is equally likely to be sampled, simple random sampling needs to be carried out in each stratum. The ratio of the number of samples in each stratum to the number of individuals in each stratum is equal to the ratio of the number of individuals in this stratum to the overall capacity.

[Typical Example 1] There are 5 towns in a region with a population of 30,000 people. The population ratio is 3:2:5:2:3. A sample of 300 people is selected from the 30,000 people and analyzed. The incidence rate of this disease is known to be related to different geographical locations, water and soil. What method should be adopted? And write down the specific process.

[ Analysis

(1) Divide 30,000 people into 5 tiers, with one township as one tier.

(2) Randomly select the samples that each town should draw in proportion to the sample size.

They are 60 people, 40 people, 100 people, 40 people, and 60 people respectively.

(3) Group 300 people together to get a sample.

2. Application of equation thinking in stratified random sampling

Mathematical modeling, logical reasoning, mathematical operations

[Typical Example 2] After the implementation of my country’s comprehensive two-child policy, a student club in a certain middle school organized a survey on the willingness to have a second child. It is known that among the married women in the town where the middle school is located who comply with the two-child policy, there are about 2,400 under 30 years old, about 3,600 between 30 and 40 years old, and about 6,000 over 40 years old. In order to understand whether there are significant differences in the willingness of women of different age groups to have a second child, the association used stratified sampling to select a sample with a capacity of N for investigation. It is known that women aged 30 to 40 were selected. The number of people is 60, then N = ________.

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