"Representation of Data" Data Analysis PPT Courseware 3

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"Representation of Data" Data Analysis PPT Courseware 3

In daily life, we often use average to express the "average level" of a set of data.

Concept one:

Generally, for n numbers x1, x2,...,xn, we call (x1+x2+...+xn)/n the arithmetic mean of these n numbers, or the average for short. Marked as x

think about it

This is how Xiao Ming calculated the average age of the Eastern Sharks players:

Average age = (16×1+18×2+21×4+23×1+24×3+26×1+29×2+34×1)÷(1+2+4+1+3+1+ 2+1)≈23.3 (years old)

Can you explain why Xiao Ming does this?

Example 1: An advertising company wants to recruit an advertising planner. It conducted three quality tests on three candidates A, B, and C. Their test scores are as shown in the table below:

(1) If candidates are decided based on the average scores of the three tests, who will be hired?

(2) Based on actual needs, the company will determine each person's test scores based on the three test scores of innovation, comprehensive knowledge and language in a ratio of 4:3:1. Who will be hired at this time?

Solution: (1) The average score of A is (72+50+88)/3=70 points.

The average score of B is (85+74+45)/3=68 points.

The average score of C is (67+70+67)/3=68 points.

Since 70>68, A will be hired.

(2) According to the meaning of the question, the test score of A is (72×4+50×3+88×1)/(4+3+1)=65.75 points.

B’s test score is (85×4+74×3+45×1)/(4+3+1)=75.875 points.

C’s test score is (67×4+70×3+67×1)/(4+3+1)=68.125 points.

Therefore candidate B will be hired

Concept two:

In practical problems, the "importance" of each data in a set of data may not be the same. Therefore, when calculating this set of data, each data is often given a "weight".

For example, 4 in Example 1 is the right to innovation, 3 is the right to comprehensive knowledge, and 1 is the right to language. It is called (72×4+50×3+88×1)/(4+3+1) as the weighted average of A’s three test scores.

Consolidation exercises

1. In order to support the Hope Project, 10 students in a certain class donated their pocket money to out-of-school children in poor areas. The amount of donation per person is as follows (unit: yuan):

10, 12, 13.5, 21, 40.8, 19.5, 20.8, 25, 16, 30. How much did these 10 students donate on average?

Solution: The average donation of these 10 students is (10+12+13.5+21+40.8+19.5+20.8+25+16+30)/10 = 20.86 yuan

Answer: How much is the average donation from these 10 students.

Extend and improve

1. Choose

(1) In a certain exam, the average score of 5 students is 82. Except for A, the average score of the other 4 students is 80. Then A’s score is ( )

(A)84 (B) 86 (C) 88 (D) 90

2. If the average of m numbers is x and the average of n numbers is y, then the average of these (m+n) numbers is ( )

A:(x+y)/2 B:(x+y)/(m+n)

C:(mx+ny)/(x+y) D:(mx+ny)/(m+n)

3. It is known that the average of data a1, a2, a3 is a, then the average of data 2a1+1, 2a2+1, 2a3+1 is ( )

(A) a (B)2a (C) 2a+1 (D) 2a/3+1

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Update Time: 2024-10-19

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