"Average and Weighted Average" PPT courseware 3

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"Average and Weighted Average" PPT courseware 3

(1) Observation and thinking

Divide an experimental field into 8 equal areas, each 100m2, and try to plant two different varieties of wheat under the same conditions such as soil fertility, fertilizer, and management. The yields are as follows:

1. From the two statistical graphs in Figure 26-1, can you tell which variety of wheat has a higher yield?

2. What number should be used to represent the yield per unit area (100m2 as the unit area) of the two wheat varieties A and B?

3. If we only consider the factor of yield, which variety is more suitable for local planting?

Since the yields of the same variety of wheat on the four test fields are different, to compare which of the two varieties has higher yield, usually compare their average yields. The average yields of variety A and variety B on the four test fields are respectively

It can be seen that variety B has a higher average yield than variety A, and variety B is more suitable for local planting.

(2) Do it

The results of 20 students of a certain grade in a mathematics competition are as follows: (unit: points)

80 85 70 75 70 75 80 80 75 85

75 80 75 70 80 75 85 70 80 75

(1) Organize data and fill in statistical tables:

(2) Find the average score of these 20 students.

Xiao Ming calculated the average based on the statistical results of question (1) of "Do it":

Is this calculation reasonable? Please share your views with your classmates.

(1) Explore together

During the holidays, Xiaohong and Xiaohui went shopping together. The prices and quantities of tomatoes purchased three times are as follows:

1. From the perspective of average price, which one is more cost-effective?

2. Thinking about what Xiaoliang and Xiaoming said, who do you think is right?

Xiaoliang said: The unit price of each purchase is the same, the total amount of the three purchases is also the same, and the average price should be the same, both (1.2+1.0+0.8)÷3=1.0 (yuan/kg).

Xiao Ming said: Although the total amount of the three purchases is the same, the amount spent is not the same, so the average price is different.

(1) Do it

Ask the whole class to visually inspect the blackboard for 20 seconds and estimate the width of the blackboard (unit: cm): record each person's estimation results.

(1) Group 8 to 10 people, group statistics on estimated data, and calculate the average of the estimated data.

(2) Summarize the number of people in each group and the average of the estimated data of each group, and calculate the average of the estimated data of the whole class.

(3) Actually measure the width of the blackboard (unit, cm) and write the result on the blackboard.

(4) Subtract the measured result from your estimated result to find the error of the estimate. Use the method of raising hands to count the estimation errors and fill in the statistical table:

(2) Let’s talk

1. Which of your estimated results, the group average or the class average, is closer to the measured result?

2. What percentage of students have an absolute value of estimation error not exceeding 10cm? What percentage of students have an absolute value of estimation error exceeding 20cm?

3. Which number is a better estimate of the actual width?

(3) Example questions

Example 2: 50 students in a class used visual inspection to estimate the length of a book (unit: cm), and organized the estimated data into groups. The results are as follows:

Using the average of these 50 data, estimate the length of the book.

(4) Practice

Now use the odometers on 10 cars to measure the length of the same section of road. The measurement results are as follows: (unit; km)

110.5 109.8 109.6 108.9 111.0

109.3 110.4 110.7 110.2 110.6:

Based on the above data, please estimate the approximate length of this section of road.

Answer

Use the arithmetic mean of 10 measurements to estimate the length of this section of road. The arithmetic mean of 10 data is 110.1 km, so the length of the road is approximately 110.1 km.

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"Average and Weighted Average" PPT Courseware 2:

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Update Time: 2024-07-06

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