<> Asia Pacific cup mathematical modeling competition

<> Explanation of knowledge points and basic models involved in data type questions

I have participated in the Asia Pacific Cup four times , Three times First Prize, On one occasion, because the computer burned out halfway, he suspended the preparation of modeling papers, so he took it Second
Prize; We are based on the present , Take a long-term view , According to social value orientation , Coach students to cross the bridge of dreams ; Comprehensively promote the award-winning goal of each student's mathematical modeling competition , Pay close attention to the key tasks of programming and mathematical model .

It can be said that the Asia Pacific cup is the most easily won mathematical modeling competition among all modeling competitions , Whether the topic of this Asia Pacific cup is to study the efficiency of the algorithm , Or to explore the laws of data , There is still a fixed range of calculation results , We can all try to describe the basic model using the data I will introduce next ：

<> Basic statistical description of data

– objective
– Basic statistical description of data
• Better identify the nature of the data , Grasp the whole picture of data .
• Central trend measurement , Data dispersion measurement , Graphical representation of data
– Central trend measurement
• mean value , Weighted arithmetic mean , median , Mode , Number of columns in
– Data dispersion measurement
• range , Quantile and quartile , Variance and standard deviation
– Graphical display of data
• Box diagram , Pie chart , Frequency histogram , Scatter diagram
Some people may say you write such a simple thing , Can't get into the eyes of the judges , sorry , I do this every year , every year First
Prize, Because before you analyze the data ： First, data processing ; Second, to understand the data from a macro perspective, this step is called the basic statistical description of the data ; The third step is to analyze the data variables specifically

<>1. Central trend measurement

– mean value （Mean）
• order x1,x2,…,xN Is a numeric attribute X of N Observations , The mean value of the value set is shown in the formula
(2-1) Shown .

– Weighted arithmetic mean （Weighted Mean）
• about i=1,…,N, Each value xi All have a weight wi.

– Median data grouping (Grouped Median)
• according to N/2 Determine the group in which the median is located

Me： median ,L： Lower limit of the median group ,Sm-1： Median group
Cumulative Frequency ,fm： Frequency of median group ,d： Group distance of median group .
– Mode (Mode)： The most frequent value in the data
– Number of columns in (Midrange)： The arithmetic mean of the maximum and minimum values in the dataset

<>2. Data dispersion measurement

– range （ Also known as full range ,Range）： Is the difference between the maximum and minimum values in the set ,
The data obtained is the minimum value after subtraction .
– Quantile （Quantile）： Points at regular intervals from the data distribution , Put data
Divided into coherent sets of basically equal size .
– variance （ Sample variance ）： Is the average of the square of the difference between each data and the average .

<>3. Graphical display of data ( Data visualization )

You have to draw in every mathematical modeling competition , But do you really understand the graphical display of data ? Do you know how to draw ? Do you know when to draw histogram , Under what circumstances are scatter plots drawn , When to draw density histogram ? Do you know why you drew , The result is also right. Why didn't you win the prize ?** Because you don't know what visual graphics to draw under any circumstances .** I'm here to tell you ： No comparison, no discrimination , Only know one , know nothing about .

– Box diagram （ Also known as box diagram ,Box-plot), Is a statistical graph used to describe the distribution of data ,
It can represent the median of observation data , Descriptive statistics such as quartile and extreme value .
– Pie chart （ Also known as circular chart or pie chart ,Pie Graph）, Usually used to represent the composition of the whole
Part and the proportional relationship between parts . A pie chart shows the size of items in a data series
Proportional relationship with the sum of items .

– Frequency histogram （ Also known as frequency distribution histogram ,Frequency Histogram）, It's in the system
A graphic representation of frequency distribution in computer science .

– Scatter diagram （Scatter Diagram）： Draw the sample data points on a two-dimensional plane or a three-dimensional space
On the room , According to the distribution characteristics of data points , Intuitively study the statistical relationship between variables and
Degree of strength .

<> Proximity measurement of nominal attributes

− Dissimilarity

• p Is the total number of properties of the object ,m Is the number of matching attributes （ Object i and j State phase
Number of attributes of the same ）
− Similarity

The discrimination methods of data dissimilarity are ：
Euclidean distance （Euclidean Distance ）： Also known as linear distance .
Manhattan distance （Manhattan Distance）： Also known as city block distance .
Minkowski distance （Minkowski Distance ）.
Chebyshev Distance （Chebyshev Distance ）： Also known as supremum distance , Define two pairs
The supremum distance between images is the maximum value of the value difference of each coordinate .

If you want to know more , And won honors in the competition , Then study hard . There is no hesitation in college study , No confusion , No tangle , Focus on the learning path under your feet , Go further and climb higher , Don't look back , Then one day, when you look at your feet, the stars are shining under your feet .

<> For learning materials and detailed algorithm procedures , mathematical model , file
return：qq2534659467

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