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"Average" data analysis PPT courseware 5
induction
Definition of arithmetic mean:
For n data x1, x2, x3,…, xn, then
It is called the arithmetic mean of these n numbers.
Representation of arithmetic mean: x=1/n(x1+x2+x3+....+xn)
Exercise 20.1
1. In order to check the length of a batch of parts, 10 pieces were taken from it and the measured lengths were as follows:
22.36 22.35 22.33 22.35 22.37
22.34 22.38 22.36 22.32 22.35
(1) What are the population, individual, sample, and sample size in this question?
(2) Estimate the average length of this batch of parts.
summary
Statistical idea: The sample mean can be used to estimate the population mean.
If the average of 4, 6, 8, x is 8, and the average of 4, 6, 8, x, y is 9, find the values of x and y.
The definition of weighted average: If the weights of n data x1, x2, x3,...,xn are respectively ω1, ω2, ω3,...,ωn, then
x1ω1+x2ω2+ x3ωn....xnωn/ω1+ ω2+ω3...+ωn is called the weighted average of these n numbers.
Representation of weighted average:
x=x1ω1+x2ω2+ x3ωn....xnωn/ω1+ ω2+ω3 …+ωn
Example 1 A company plans to recruit an English translator. Two candidates A and B were tested on English proficiency in listening, speaking, reading and writing. Their scores (percentage system) are as follows:
(1) If this company wants to recruit a translator with strong oral skills, the listening, speaking, reading and writing scores are determined according to the ratio of 3:3:2:2. Calculate the average score of the two candidates and calculate it from their Based on grades, who should be admitted?
(2) If this company wants to recruit a translator with strong translation skills, the listening, speaking, reading and writing scores are determined according to the ratio of 2:2:3:3. Calculate the average score of the two candidates and calculate it from their Based on grades, who should be admitted?
Explore
(1) Admit A, (2) Admit B. Why is this?
The meaning of weight: Weight reflects the relative "importance" of data.
Class summary
1Main knowledge content:
If the weights of n numbers x1, x2, x3,…,xn are respectively ω1, ω2, ω3,…,ωn, then
x1ω1+x2ω2+ x3ωn....xnωn/ω1+ ω2+ω3...+ωn is called the weighted average of these n numbers.
The weight of data can reflect the relative "importance" of the data.
2 Calculate the average of sample data using weighted average
3. Carefully understand the meaning of weighted average weight.
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