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"Weighted Average" PPT Courseware 3
Concept: weighted average
Generally, if among k numbers, x1 appears w1 times, x2 appears w2 times, ..., xk appears wk times (at this time w1+w2+...+wk=n), then the weighted average of these n numbers for
In a set of data, w1/n, w2/n, w3/n,...wk/n are called the weights of these k data.
Example 1: In order to examine the height of 12-year-old boys in the county, 240 people were selected and their heights (unit, centimeters) were measured as shown in the table below
Calculate the mean of this sample and estimate the average height of 12-year-old boys in the county
Solution: The average height of a 12-year-old boy is (140×2+141×10+142×16+143×56+144×70+145×56+146×20+147×8+148×2)÷240=144 (centimeter)
Answer: The average height of 12-year-old boys in the county is 144 (cm)
Example 2: The school’s small press team plans to recruit a young reporter. Three candidates, Xiaoying, Xiaoliang and Dagang, were tested on their final exam results, on-site essay competition, and oral expression ability. Their scores were as follows:
(1) If the ratio of 4:4:2 is determined and the total personal scores of the three candidates are calculated, who should be admitted based on their scores?
(2) If you want to recruit a reporter with strong oral expression skills, and the score is determined according to the ratio of 2:3:5, calculate the total personal score of the three candidates. Based on their scores, who should be admitted?
weighted average
Main knowledge content:
If there are n numbers x1, x2, x3,..., the importance of xn is expressed in continuous ratios:
f1; f2; f3;······, fn Then f1, f2, f3,······fn are called weights
The weighted average of these n numbers is:
x1f1+x2f2+···+xnfn/f1+f2+······,+fn
The "right" of data can reflect the relative "importance" of the data.
The difference and connection between the arithmetic mean and the weighted average are:
1. The arithmetic mean is a special case of the weighted average (it is special in that the weights of each item are equal).
2. When the weights of the various items are not equal in actual problems, the weighted average must be used to calculate the average; when the weights of the items are equal, the arithmetic mean must be used to calculate the average. The two cannot be confused.
summary
What knowledge have you learned? What questions do you still have?
Operation:
Matching questions 1 to 5 on page 44; questions 1, 2, and 3 on page 45.
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"Average and Weighted Average" PPT courseware 3:
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"Average and Weighted Average" PPT Courseware 2:
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"Average and Weighted Average" PPT courseware:
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