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Selected candidates prepare for the exam: three "pithy formula" to help you solve the problem of proportion mixing in the analysis of travel survey data

2023-03-06 09:16:35 |Source: Shaanxi Zhonggong Education

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In the analysis of survey data, the proportion mixing problem is one of the important test points. Today, CUHK Education uses three "pithy formula" to teach everyone to quickly solve the proportion mixing problem.

  Question type characteristics  

The proportion of a to A is P1, the proportion of b to B is P2, and the proportion of (a+b) to (A+B) is P, where P1 and P2 are partial proportions, and P is the overall proportion. Problems like this are called proportion mixing problems.

  Common Applications  

（1） Given P1 and P2, calculate the value of P

Formula 1: The overall proportion is between partial proportions

Example 1

In 2020, there will be 243810 doctoral students in secondary and higher education institutions nationwide, of which the minority students will account for 4.23%; There are 1236008 master students in school, of which the minority students account for 4.89%.

Question: In 2020, the proportion of ethnic minority postgraduates in China's secondary and higher education institutions will be about:

A.4.03% B.4.23% C.4.68% D.4.89%

[Chinese public resolution] The answer is C. According to the materials, the minority nationality accounts for 4.23% of the doctoral students and 4.89% of the master students. The figure is the minority nationality proportion of the graduate students, that is, the number of minority nationalities in the graduate students=the number of minority nationalities in the doctoral students+the number of minority nationalities in the master students, and the number of graduate students=the number of doctoral students+the number of master students. The three ratios conform to the additive relationship between the numerator and denominator. The figure is the overall ratio, which can be obtained according to formula 1, and the proportion is between 4.23% and 4.89%, so C is selected for this question.

Formula 2: The proportion of the whole is closer to that of the part with large overall value

Example 2

In 2020, China's total import and export of goods will be 24574.1 billion yuan. Among them, the export volume of goods was 14125.6 billion yuan, down 1.8% year on year, and the export volume of general trade was 7545.6 billion yuan, accounting for 53.4% of the total export volume; The import of goods was 10448.5 billion yuan, down 13.2% year on year. The import of general trade was 5732.3 billion yuan, accounting for 54.9% of the total import.

Question: What is the proportion of China's total imports and exports of general trade in China's total imports and exports of goods in 2020?

A.54.9% B.54.6% C.54.1% D.53.4%

[Chinese public resolution] The answer is C. According to the materials, the proportion of general trade exports in total exports is 53.4%, and the proportion of general trade imports in total imports is 54.9%. The figure is the proportion of general trade imports and exports in total imports and exports of goods in China, that is, total imports and exports of general trade=general trade exports+general trade imports, total imports and exports of goods=exports of goods+imports of goods, The three ratios correspond to the additive relationship between molecules and denominators. The figure is the overall ratio. According to the formula 1, the proportion is between 53.4% and 54.9%, excluding A and D. Since the export of goods (14125.6 billion yuan) is greater than the import of goods (10448.5 billion yuan), the range can be narrowed down to That is, 53.4%~54.15%, so select C for this question.

（2） Given P1, P2 and P, calculate the ratio between A and B

Formula 3: The ratio obtained by cross difference of specific gravity is equal to the ratio of the overall value in the corresponding part

Example 3

The survey results of a city's statistics on the "revision and legislation of smoking control regulations in public places" in 2020 show that 95.2% of the respondents support, 2.9% do not support, and 1.9% do not care; 97.0% of female respondents expressed support, and 92.7% of male respondents expressed support.

Question: In this survey, the proportion of the number of female citizens interviewed in the total number of respondents is:

A.36.7% B.41.9% C.58.1% D.63.3%

[Chinese public resolution] The answer is C. 97.0% of female interviewees expressed support, 92.7% of male interviewees expressed support, and 95.2% of the interviewees finally expressed support. If the proportion before and after mixing is known, the ratio of the number of female interviewees to male interviewees can be obtained according to Formula 3. The specific operations are as follows:

Conclusion: To solve the mixed proportion problem, you need to be able to quickly determine the type of question, and then combine the above three pithy formula to easily solve the question. Please continue to pay attention to public education for more skills to be unlocked later.

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