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why can't scatter plot and broken-line graph be used to present the favorite sports of the students in a class?
- scatter diagram can only show the relationship between two kinds of numerical data, but the data involved are non-numerical and of the same kind.
- Also, the data are not related to time, broken-line graph is not suitable to present the data. Thus scatter diagram and broken-line graph cannot be used.
In a canteen, the manager wants to collect the opinions of customers about the quality of service on a day. why would the following method not give a representative sample?
I. Questionnaires will be sent to the first 20 customers who enter the canteen.
the first 20 customers may enjoy good quality of service cuz there are only a few people in that period. The staff have more time to serve the customers. Also, the environment is more comfortable and the customers would enjoy more. Their opinions would be different from those of customers from other periods.
Questionnaires will be sent to customers who have lunch in the canteen from 12 pm to 2 pm.
the lunch hour is usually 12-2pm. It is the peak hour of the canteen. Customers would not want to wait a long time. To prevent them from leaving the canteen before having lunch there, the staff would speed up their work and the quality of service would drop. Thus their opinions would be different from those of customers from other periods.
III. Questionnaires are placed next to the cashier for the customers to take.
the customers who have strong opinions about the quality of service are more likely to complete the questionnaire. their opinion may not represent the majority of the customers.
the government has collected the opinions of citizens about smoking ban in public areas by interviewing the non-smoking citizens in a certain public area for one week. Based on the data obtained, the government concludes that a majority of citizens agree to smoking ban in public areas.(a) Is the sample a good representation of the opinions of citizens about smoking ban in public areas? (b) Suggest a more appropriate sampling method.
- (a) The sample is not a good representation of the opinions of citizens about smoking ban in public areas because all the interviewees were non-smoking citizens who tend to agree smoking ban in public areas.
- (b) The government randomly selects a number from 1 to 10 (say 7). Using this number, he first interviews the 7th pedestrian, then interviews every 10th pedestrian thereafter in the area for
- one week.
Based on the passing percentage of chinese, the principal of school A claims that the number of students who passed Chinese examination in their school is greater than that in school B. Do you agree? Explain briefly.
- No, it is because the numbers of students in two schools are unknown. It may be the case
- that the number of students in school B is
- much more than that in school A.
The profits of a company in 2006 and 2010 are $20 million and $25 million respectively. Based on the above information, someone claims that the net profit of the company in 2010 is greater than that in 2006. Do you agree? Explain briefly.
- No, it is because we can only say that the profit of the company in 2010 is greater than that in 2006.
- Without the expenditures in 2006 and 2010, we do not know the net profits in 2006 and 2010.
The average daily times the students in a school spend on online games are to be investigated. In each of the following cases, suggest a possible problem and an improvement: Every 6th student of this school leaving a cyber café nearby is asked to fill in a questionnaire.
- Possible problem: Those students in the cyber café will probably spend more time on online
- games than those who have not gone to the cyber café.
- Improvement: Every 6th student leaving the school is asked to fill in a questionnaire.
Questionnaires will be sent to students through the email service. The students have the freedom to reply or not.
- Possible problem: Those students who can access to the Internet easier or frequently are probably more likely to complete the survey than those who cannot.
- Improvement: Questionnaires will be sent to students in classes and collected at the end of
- the lessons.
State a possible problem for each of the following statements:Over
80% of the students in our tutorial centre got grade A in a public examination.
The number of students in that tutorial centre was unknown, it may have been very small. Also, some students who got grade A may have just attended one or two lessons, and the tutorial centre still considered them as their students.
State a possible problem for each of the following statements:In a quiz, the average score of 30 students in a class is 60.
average can refer to mean, mode or median