We often use the average score of each subject to compare the grades between classes and classmates. To get the average score of each subject is to get the average.
Average is widely used in daily life and work, such as finding the average height and average temperature on a certain day.
The basic quantitative relationship of the average problem is:
Total quantity/total number of copies = average value
The key to solving the average problem is to determine the "total number of copies" corresponding to the "total amount" and then divide the total amount by the total number of copies to get the average.
Example 1: The students in Class Two (1) are divided into three groups to plant trees. The first group of 8 people planted 80 trees. In the second group, 6 people planted 66 trees. The third group of 6 people planted 54 trees. How many trees are planted per person on average?
Analysis and answer: Because the students in Class Two (1) plant trees in three groups, we can know from the question that the "average range" is three groups, and the number of people is average, so the required conditions are the total number of trees planted in three groups and the total number of people in three groups. The total number of plants planted in the three groups is 80+66+54=200, and the total number of people is 8+6+6=20, so the average number of plants in each group is 200/20 = 10.
Exercise 1
1, the TV factory produced 3,300 TV sets before April 10, and 6,300 TV sets 20 days after April. How many TV sets are produced on average every day this month?
Xiaoming took part in the math exam. The average score of the first two times was 85, and the total score of the last three times was 270. Ask Xiao Ming what is the average score of these five exams?
Students in Class 3 and Class 2 (1) are divided into three groups to plant trees. The first group has 8 people, with an average of each person 10 tree. The second group consists of 6 people, with an average of 1 1 tree; In the third group, there are 6 people, each of whom plants 9 trees on average. How many trees are planted in Class Two (1)?
Example 2: Teacher Wang measures the height of the students of the fourth-grade badminton team. Height of two students 153 cm, one height 152 cm, two heights 149 cm and two heights 147 cm. Find the average height of the students in the fourth grade badminton team.
Analysis and solution: this problem can be solved according to the general idea, that is, divide the total height by the total number of people. This problem can also be solved by assuming the average value. It is easy to find that the height of students is around 150 cm. It can be assumed that the average height is 150 cm, as the reference number, and "base number+sum of differences between each number and base number ÷ number of copies = average number" can be used.
( 153×2+ 152+ 149×2+ 147×2)÷(2+ 1+2+2)= 150cm。
Or:150+(3× 2+2-12-3× 2) ÷ (2+1+2+2) =150cm.
Exercise 2
Seven students from Class 5 (1) 1 took part in the math contest. Two students got 99 points, three students got 96 points, and the other two students got 97 points and 89 points respectively. What is the average score of these seven students?
2. The weekly temperatures measured by the Meteorological Team at 8: 00 am every day are as follows: 13℃, 13℃, 14℃, 15℃, 14℃, 16℃. Find the average temperature of a week.
3. There are eight elderly people in the nursing home, aged 78, 76, 77, 8 1, 78, 78, 76 and 80 respectively. Find the average age of these eight old people.
Example 3: The road from the top of the mountain to the bottom of the mountain is 36 kilometers long. It takes 4 hours to get to the top of the mountain by car, and only 2 hours to return to the bottom of the mountain along the original road. Find the average speed of this car going back and forth.
Analysis and solution: Find the average round-trip speed, the round-trip distance should be divided by the round-trip time, the round-trip distance is 36 × 2 = 72km, and the round-trip time is 4+2=6 hours. So the average speed of this car is 72÷6= 12 km.
Exercise 3
1, Xiao Qiang's home is away from school1200m. It takes him 15 minutes to go to school in the morning and 10 minutes to go home from school. Find the average speed of Xiao Qiang round trip.
Li went to the mountain to collect medicine. When climbing the mountain, he walked 50 meters per minute, 18 minutes to reach the top of the mountain. When he went down the mountain, he returned along the original road and walked 75 meters per minute. Find the average speed of Uncle Li going up and down the mountain.
3. Xiao Liang walked 2 kilometers per hour when going up the mountain and 6 kilometers per hour when going down the mountain. So, how many kilometers is his average speed in the whole process of going up and down the mountain?
Exodus 4: Li Hua took part in the sports standard test, with an average score of 85 in five items. If the throwing score is not included, the average score is 83 points. How much did Li Hua invest?
Analysis and solution: First get five total scores: 85×5=425 points, then calculate four total scores: 83×4=332 points, and finally subtract four total scores from the five total scores, which is equal to Li Hua's throwing performance: 425-332 = 93 points.
Exercise 4
1, Xiaojun participated in three math competitions, with an average score of 84. It is known that the average score of the first two times is 82 points. How many points did he get in the third exam?
2. At the time of Xiaoli's final exam, her average score in four subjects was 92 before her math scores were announced. After her math scores were announced, her average score dropped by 1 point. How many points did Xiaoli get in the math exam?
There was a foreign language exam in the class, but Li Xing didn't take it because of illness. The average score of other students was 95, and the next day he made up the exam with 65. If you add Li Xing's score, the average score of the whole class is 94. How many people are there in this class?
Example 5: If the average age of four people is 23, none of them is younger than 18. How old are people at that age?
Analysis and answer: Because the average age of four people is 23 years old, the total age of four people is 23×4=92 years old; We also know that all four people are under 18 years old. If three of the four people are 18 years old, we can ask that the other person's age may be 92- 18× 3 = 38 years old.
Exercise 5
1, if the average age of three people is 22 years old, and no one is younger than 18 years old, what are the ages of the three people?
2. If the average age of four people is 28, no one is over 30. So how old is the youngest person?
3. If the average age of four people is 25 years old, and none of them is younger than 16 years old, these four people are not equal in age. What about age?