Teaching objectives:
1, knowledge and skills:
(1) correctly understand the concept of random sampling, and master the general steps of drawing lots and the random number table method;
2, process and method:
(1) Be able to ask some valuable statistical questions from real life or other disciplines;
(2) In the process of solving statistical problems, learn to take samples from the population by simple random sampling.
3. Emotion, attitude and values: By asking statistical questions in real life and other disciplines, we can understand the relationship between mathematical knowledge and the real world and the knowledge of various disciplines, and realize the importance of mathematics.
4. Emphasis and difficulty: correctly understand the concept of simple random sampling, master the steps of lottery method and random number method, and flexibly use relevant knowledge to extract samples from the population.
Teaching philosophy:
Suppose you are a food hygiene worker and want to inspect a batch of biscuits in small packages in a food store. what are you going to do？
Obviously, you can only take a certain number of biscuits as samples for inspection. (Why? ) So, how should we get samples?
Explore new knowledge
First, the concept of simple random sampling
Generally speaking, it is assumed that a population contains n individuals, from which n individuals are selected as samples (n≤N). If the probability of each individual in the group being drawn is equal every time, this sampling method is called simple random sampling, and the samples thus drawn are called simple random sampling.
Explain that simple random sampling must have the following characteristics:
(1) Simple random sampling requires that the total number of samples n to be sampled is limited.
(2) The number n of simple random samples is less than or equal to the number n of the sample population.
(3) Extract simple random samples from the population one by one.
(4) Simple random sampling is a kind of sampling that cannot be put back.
(5) The probability of sampling each individual by simple random sampling is n/n 。
Thinking?
Are the following sampling methods simple random sampling? Why?
(1) Take 50 individuals from an infinite number of individuals as samples.
(2) There are 100 parts in the box, of which 10 parts are selected for quality inspection. In the sampling operation, a part is randomly selected for quality inspection, and then it is put back in the box.
Second, the lottery method and random number method
1, the definition of lottery.
Generally speaking, the lottery method is to number n individuals in the population, write the numbers on the digital labels, put the digital labels into a container, and after stirring evenly, extract one digital label from it every time and extract it for n times continuously to get a sample with a capacity of n. 。
Explain the general steps of drawing lots:
(1) Number the individuals in the population.
(2) draw lots continuously to obtain the sample number.
Thinking?
What do you think are the advantages and disadvantages of drawing lots? Is it convenient to draw lots when there are many individuals in the group?
2, the definition of random number method:
Sampling with random number table, random number dice or computer-generated random numbers is called random number table method, and only the random number table method is introduced here.
How to generate samples with random number table? Let's use an example to illustrate. Suppose we want to check whether the quality of 500g bagged milk produced by a company is up to standard. Now we take 60 bags from 800 bags for inspection. When sampling with a random number table, we can follow the following steps.
The first step is to number 800 bags of milk, which can be numbered 000,001,…, 799.
Step 2: Select any number in the random number table, for example, the number 7 in row 8 and column 7 (for convenience of explanation, take row 6 to 1 0 in the table below).
16 22 77 94 39 49 54 43 54 82 17 37 93 23 78
84 42 17 53 3 1 57 24 55 06 88 77 04 74 47 67
63 0 1 63 78 59 16 95 55 67 19 98 10 50 7 1 75
33 2 1 12 34 29 78 64 56 07 82 52 42 07 44 38
57 60 86 32 44 09 47 27 96 54 49 17 46 09 62
87 35 20 96 43 84 26 34 9 1 64
2 1 76 33 50 25 83 92 12 06 76
12 86 73 58 07 44 39 52 38 79
15 5 1 00 13 42 99 66 02 79 54
90 52 84 77 27 08 02 73 43 28
Step 3, read right from the selected number 7 (the reading direction can also be left, up, down, etc.). ) get a three-digit 785. Since 785 < 799, it means that 785 is in the crowd, take it out; Keep looking to the right and get 9 16. Because 9 16 > 799, it was removed. Continue reading to the right, take out 567,199,507, …, and so on until all 60 samples are taken out, so we get a sample with a capacity of 60.
Explain the steps of random number table method:
(1) Number the individuals in the population.
(2) Select the starting number in the random number table.
(3) read the sample number.
Detailed analysis of examples
Example 1: When people play bridge, they randomly determine a washed playing card as the starting card. At this time, when moving cards in sequence, for any family, draw 13 cards from 52 cards. Is this sampling method a simple random sampling?
[Analysis] The essence of simple random sampling is to randomly select samples from the population one by one, where only the starting cards are randomly determined. Although all the other cards are played one by one, whose hand has been determined, so it is not a simple random sampling.
Example 2: Workers in the workshop process 65,438+000 shafts. In order to know the diameter of this shaft, 65,438+00 shafts should be taken and measured under the same conditions. How to sample simple random sampling?
Analysis: Simple random sampling generally adopts two methods: lottery method and random number table method.
Solution 1: (Draw lots) Number the 100 axis as 1, 2, …, 100, and make numbers with the same size and shape, write down the numbers of 100 respectively, put them together, stir them evenly, and then extract them continuously.
Scheme 2: (Random number table method) Number the 100 axis as 00, 0 1, …99, and select a starting position in the random number table. For example, starting from the number 1 in line 2 1, the axis 10 is selected as 68, 34, 30, 65449.
Course summary
1. Simple random sampling is the simplest and most basic sampling method. There are two ways to choose an individual: put it back and not put it back. In the sampling survey, we use non-return sampling. Commonly used simple random sampling methods are lottery and random number.
2. The advantage of drawing lots is simple, but the disadvantage is that when the overall capacity is large, it is time-consuming, laborious and inconvenient. If the labels are mixed unevenly, it will lead to unfair sampling. The advantages of the random number table method are the same as those of the lottery method, but the disadvantage is that it is still inconvenient when the overall capacity is large, but it is fairer than the lottery method. Therefore, these two methods are only suitable for sampling types with small overall capacity.
3. The possibility of extracting each individual by simple random sampling is equal, which is n/N, but here we must distinguish the possibility of extracting each individual, the possibility of extracting each individual for the nth time and the possibility of extracting a specific individual for the nth time to avoid mistakes in solving problems.
Evaluation design
1. In order to know the height of 240 students in the whole school, 40 students were selected for measurement. The following statement is correct.
A. The total number is 240 B, and the individual is each student.
C, the sample is 40 students, and the sample size is 40.
2. In order to correctly handle the length of a batch of parts, the length of 200 parts was sampled. In this problem, the length of 200 parts is ().
A, the whole B, the individual is each student
C, total sample D, sample size
There are 200 individuals in a group. If a sample with a capacity of 20 is selected by simple random sampling, the possibility of selecting a specific individual is.
4. Randomly select 2 from 3 boys and 2 girls, and check their math scores. The probability that all girls are drawn is.