statistics

Statistical chart

(1) Importance

* A graph representing the quantitative relationship between related quantities with dotted lines is called a statistical graph.

(2) Classification

1 bar chart

Use a unit length to represent a quantity, draw straight lines with different lengths according to the quantity, and then arrange these straight lines in a certain order.

Advantages: It is easy to see the quantity of each.

2 broken line statistical chart

Use a unit length to represent a quantity, draw points according to the quantity, and then connect the points in turn with line segments.

Advantages: it can not only represent quantity, but also clearly represent the change of quantity.

3 fan-shaped statistical chart

Use the area of the whole circle to represent the total, and use the sector area to represent the percentage of each part in the total.

Advantages: It clearly shows the relationship between each part and the whole.

Three applications

1, solve the problem of addition application:

An application problem of finding the total number: what is the known number A, what is the number B, and what is the sum of the two numbers A and B.

Find a number greater than the number. Application problem: Know what A number is, how much more B number is than A number, and find what B number is.

2. Solve the application problem of subtraction:

A Finding the residual application problem: removing a part from the known number and finding the residual part.

The application problem of finding the difference between two numbers by B: Given the numbers of A and B, find how much A is more than B, or how much B is less than A. ..

The application of c to find the number less than the number: what is the known number a, how much is the number b less than the number a, and how much is the number B.

3. Solve the multiplication application problem:

An application problem of seeking the sum of common addends: find the sum of the same addend and the same addend.

The application problem of finding the multiple of a number is: how many times is one number, how many times is another number, and how much is another number?

4, solve the problem of division:

A divide a number into several parts on average, and find out how much each part is: know a number, divide it into several parts on average, and find out how much each part is.

B. Find an application problem, in which one number contains several other numbers: given a number, how many copies are there in each number, and how many copies can you find?

C the application problem of finding a number that is several times that of another number: given the number A and the number B, finding a larger number is several times that of a smaller number.

D know how many times a number is, and find the application problem of this number.

5. Common quantitative relationships:

Total price = unit price × quantity distance = speed × time

Total amount of work = working hours × total output of work efficiency = single output × quantity

6. Typical application problems

Compound application problems with unique structural characteristics and specific problem-solving rules are usually called typical application problems.

(1) average problem: average is the development of equal division.

The key to solve the problem is to determine the total quantity and the corresponding total number of copies.

Arithmetic average: Given several unequal quantities of the same kind and the corresponding number of copies, find the average of each number of copies.

Quantity relationship: sum of quantity ÷ quantity = arithmetic average.

(2) Normalization problem: Two interrelated quantities are known, one of which changes, and the other changes with it, and the changing law is the same. This problem is called standardization. This kind of problem can also be solved by proportional knowledge.

(3) Sum problem: the number of units and units of measurement, as well as different units (or units) are known, and the number of units (or units) can be obtained by finding the total.

Features: Two related quantities, one changing and the other changing, have opposite changing rules and are connected by inverse ratio algorithm.

Example: To build a canal, it was originally planned to build 800 meters a day, and it was completed in six days. Actually, it took four days to fix it. How many meters are repaired every day?

Analysis: Because of the length of daily maintenance, we must first find out the length of the canal. Therefore, this kind of application problem is also called "inductive problem". The difference is that "normalization" first finds a single quantity, and then finds the total quantity. The general problem is to find the total quantity first, and then find the single quantity. 800×6÷4= 1200 (m)

(4) Travel problem: About walking, driving and other issues, it is generally to calculate the distance, time and speed, which is called travel problem. To solve this kind of problems, we must first understand the concepts of speed, time, distance, direction, speed sum and speed difference, and understand the relationship between them, and then answer them according to the laws of this kind of problems.

The key and law of solving problems;

Go in the opposite direction at the same time: distance = speed x time.

Walking in the opposite direction at the same time: meeting time = speed and x time.

(5) Planting Trees: This kind of application problem is titled "Planting Trees". Any application problem of studying the four quantitative relations of total distance, plant distance, number of segments and number of plants is called tree planting problem.

The key to solving the problem: to solve the problem of planting trees, we must first judge the terrain and distinguish whether the graph is closed, so as to determine whether to plant trees along the line or along the perimeter, and then calculate according to the basic formula.

Law of problem solving: plant trees along the line.

Tree = number of segments+1 tree = total distance ÷ distance between plants+1

Plant spacing = total distance present (tree-1)

Total distance = plant spacing × (tree-1)

Planting trees along the periphery

Tree = total distance ÷ plant distance

Plant spacing = total distance.

Total distance = plant spacing × trees

Example: 30 1 poles are buried along the highway, and the distance between every two poles is 50m. Later, it was completely revised and only 20 1 was buried. Find the distance between two adjacent ones after modification.

Analysis: this question is to bury telephone poles along the line, and the number of telephone poles is reduced by one. The formula is 50× (301-1) ÷ (201-1) = 75 (m).

(6) The problem of chickens and rabbits: The total number of heads and legs of chickens and rabbits is known. How many chickens and rabbits are there? It is often called "the problem of chickens and rabbits", also known as the problem of chickens and rabbits in the same cage.

The key to solving the problem: generally, the problem of chicken and rabbit is solved by hypothesis, assuming that all animals are one kind (for example, all chickens or rabbits), and then according to the different number of legs, the number of heads of a certain kind can be calculated.

Example: A chicken and a rabbit have 50 heads, 170 legs in the same cage. How many chickens and rabbits are there?

The number of rabbits is (170-2×50)÷2=35 (only).

The number of chickens is 50-35= 15 (only)

(b) Application of scores and percentages

1, fractional multiplication problem:

Refers to the application of knowing a number and finding its score.

Features: The quantity and fraction of the unit "1" are known, and the actual quantity corresponding to the fraction is found.

The key to solving the problem is to accurately judge the number of units "1". Find the score corresponding to the required question, and then formulate it correctly according to the meaning of multiplying a number by a score.

3. Application of fractional division:

Find the fraction or percentage of one number to another.

Features: Knowing one number and another, find the fraction or percentage of one number. "One number" is a comparative quantity, and "another number" is a standard quantity. Find a fraction or percentage, that is, find their multiple relationship.

The key to solving the problem: start with the problem and find out who is regarded as the standard number, that is, who is regarded as "unit one" and who is the bonus compared with the number of unit one.

A is the fraction of B (what percentage): A is the comparative quantity, and B is the unit "1", divided by B. ..

How much more (or less) is A than B? The difference is ÷ 1

Given the fraction (or percentage) of a number, find the number.

Features: Knowing an actual quantity and its corresponding fraction, find the quantity with the unit of "1".

The key to solve the problem is to accurately judge the number of units "1". The quantity of unit "1" is regarded as the equation of X according to the meaning of fractional multiplication or the equation of fractional division, but the known actual quantity corresponding to the fractional rate must be accurately found.

4 Attendance rate

Germination rate = number of germinated seeds/number of experimental seeds × 100%

Wheat flour yield = flour weight/wheat weight × 100%.

Product qualification rate = number of qualified products/total number of products × 100%.

Employee attendance = actual attendance/attendance × 100%

Five engineering problems:

It is an applied problem to explore the relationship among total workload, work efficiency and working hours.

The key to solving the problem: regard the total amount of work as the unit "1", and the work efficiency is the reciprocal of the working time, and then use the formula flexibly according to the specific situation of the topic.

Quantitative relationship:

Total amount of work = working efficiency × working time

Work efficiency = total workload ÷ working hours

Working hours = total amount of work ÷ working efficiency

Total workload ÷ work efficiency = cooperation time

6 pay taxes

The taxes paid are called taxes payable.

The ratio of taxable amount to various incomes (sales, turnover and taxable income) is called tax rate.

* Interest

Money deposited in the bank is called principal.

The extra money paid by the bank when withdrawing money is called interest.

The ratio of interest to principal is called interest rate.

Interest = principal × interest rate× time