Everyone has a lot of knowledge in daily study, right? Knowledge point is the basic unit of transmitting information and plays an important role in improving learning navigation. Mastering knowledge points will help everyone to study better. The following is a summary of the compulsory mathematics 3 statistics knowledge points I collected for you. Welcome to reading. I hope you will like it.
Mathematics compulsory 3 statistical knowledge points summary
Random sampling
simplerandom sampling
Generally speaking, suppose a population contains n individuals, from which N individuals are taken as samples one by one (N
This method is usually only used when the difference between the whole units is small and the number is small.
1. Common methods of simple random sampling:
(1) draw lots;
(2) Random number table method;
Draw lots:
Step 1: Number all n individuals in the population from 0 to (N- 1);
Step 2: prepare n numbers and mark them respectively, put the numbers into a container and stir them evenly, then extract one number at a time, take it n times in a row, and don't put it back;
Step 3: Take N individuals corresponding to the numbers on N labels as samples.
(2). Random number table method:
Step 1: Number all n individuals in the population from 0 to (N- 1).
Step 2: select the starting number in the random number table;
Step 3: Start with the selected number and read in a certain direction. If the number obtained is greater than the total number or is taken out repeatedly with the previous number, it is taken out within n.
Number, and so on, until it is full, take the individuals corresponding to these n numbers as samples.
systematic sampling
When there are multiple individuals in the group, the group is divided into several balanced parts, and then an individual is extracted from each part according to predetermined rules to get the required samples. This kind of sampling is called systematic sampling.
(1) First number the n individuals in the population. Sometimes, you can use your personal number directly.
(2) Determine the segmentation interval K. Divide the numbers evenly, where k (sampling distance) =N (overall size) /n (sample size).
When k is not an integer, some individuals are excluded from n until it is an integer.
(3) The first paragraph uses simple random sampling to determine the starting number.
group sampling
(1) Definition: Divide people into several types according to their attribute characteristics, and then randomly select certain samples in each type according to the proportion. This sampling method is usually called stratified sampling.
(2) The scope of application of stratified sampling:
When the population consists of several parts with obvious differences, stratified sampling is often used.
Estimation of population distribution by frequency distribution of samples
The ratio of the frequency of all data (or data group) in a (1) sample to the sample size is the frequency of the data, and the variation law of the frequency distribution of all data (or data group) is called frequency distribution, which can be expressed by frequency distribution table, frequency distribution histogram, frequency distribution line graph, stem leaf diagram, etc.
(2) making a histogram of frequency distribution:
Find the range, that is, the difference between the maximum value and the minimum value in a set of data;
Determine the interval and the number of groups;
Packet data;
Column frequency distribution table;
Draw a histogram of frequency distribution.
In the histogram of frequency distribution, the vertical axis represents the distance of frequency groups, the frequency of data falling in each group is represented by the area of each small rectangle, and the sum of the areas of each small rectangle is 1.
General density curve
(1) frequency distribution line chart: connect the midpoints of each small rectangle in the frequency distribution histogram to get the frequency distribution line chart;
(2) Overall density curve: If the sample size increases, the number of groups divided in the graph increases and the distance between groups decreases, the corresponding frequency line graph will be closer to a smooth curve, which is statistically called the overall density curve.
(3) Stems and leaves diagram: There is another diagram used to represent data in statistics called Stems and leaves diagram. The stem refers to the middle column of numbers, and the leaves are the numbers that grow from the side of the stem.
When the sample data is small, it is best to use the stem-leaf diagram to represent the data. The stem-leaf diagram has two outstanding advantages: first, it can better retain the original data information; Second, it can display the distribution of data, which is convenient for recording and representation.
Digital characteristics of samples
1, mode: the data with the highest frequency in a group of data is called mode.
2. Median: arrange a group of data from small to large (or from large to small) in turn, and call the intermediate data (or the average of two intermediate data) as the median, which divides the sample data into two parts with the same number.
3. Average value: the average value of x 1, x2 and xn is x=n 1(x 1+x2++xn).
Because the pattern can only describe the number of times a certain data appears, the median is insensitive to the extreme value, and the average value is affected by the extreme value, these factors restrict the accuracy of estimating the overall digital features only by these digital features.
4. Standard deviation and variance
Standard deviation is the most commonly used statistic to investigate the dispersion of sample data. The standard deviation is the ratio of the sample data to the average.
Methods The mode, median and average were estimated by histogram of frequency distribution.
1, mode: take the abscissa of the midpoint of the highest rectangle bottom as the mode;
2. Median: In the histogram of frequency distribution, the abscissa of the intersection of the left and right dividing lines with equal area and the X axis is called median.
3. Average value: the average value is the center of gravity of the histogram of frequency distribution, which is equal to the sum of the areas of each small rectangle multiplied by the abscissa of the midpoint at the bottom of the small rectangle.
Further reading
First, the meaning of random events
1. Inevitable event: an event that must occur under certain conditions.
2. Impossible event: an event that will never happen under certain conditions.
3. Random events: events that may or may not occur under certain conditions.
Note: capital letters a, b and c are generally used.
Second, probability and frequency.
Under the same conditions, when the same experiment is repeated a lot, the frequency of random event A will swing around a constant, that is, the frequency of random event A is stable. At this time, we call this constant the probability of random event A and write it as P(A).
Third, mutually exclusive events.
1, two events that cannot happen at the same time are called mutually exclusive events;
2. If any two events are mutually exclusive events, they are said to be mutually exclusive.
3. If events A and B are mutually exclusive, then the probability of event A+B is equal to the sum of the probabilities of events A and B. ..
4. If the events are mutually exclusive, there are: P(A+B)=P(A)+P(B).
5. Opposing events: If one of the two mutually exclusive events is bound to happen, these two events are called opposing events. The opposing event must be mutually exclusive events, but mutually exclusive events is not necessarily an opposing event.
Fourth, the basic nature of probability
The values of 1. probability are all within [0, 1], that is, 0 1, the probability of impossible events is 0, and the probability of inevitable events is 1.
Classical probability of verb (abbreviation of verb)
Definition of 1: A probability model with the following two characteristics is called a classical probability model, which is referred to as a classical probability model for short.
(1) The number of possible basic events in the experiment is limited.
(2) The possibility of each basic event is equal.
2. Probability formula of classical probability type
P(A)= total number of basic events =nm.
Six-geometric probability
1. Concept: If the probability of each event is only proportional to the length (or area or volume) of the event area, such a probability model is called geometric probability model, or geometric probability model for short. The basic characteristics of geometric probability model are:
(1) There are infinitely many possible results (basic events) in the experiment;
(2) The possibility of each basic event is equal.
2. The formula for calculating the probability of event A in geometric probability.
3. The probability of random events can be estimated by simulation.
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