1. An advertising agent uses the following diagram to present the sales volumes of two brands of fruit juice last month.
(a) What was the sales volume of each brand of fruit juice last month?
(b) What message do you think the advertising agent is trying to give?
2. The figure shows the selling price of a digital video recorder in the past six months.
(a) What was the percentage decrease in the selling price of the digital video recorder over the past six months?
(b) Do you think the accompanying statement of the above figure is misleading? Explain briefly.
3. A merchant uses the following diagrams to show the sales volumes of two models of cars.
(a) What was the increase in the sales volume of each car model from years 2008 to 2010?
(b) What was the percentage increase in the sales volume of each car model from years 2008 to 2010?
(c) What message do you think the merchant is trying to give?
4. The figure shows an advertisement of company A.
(a) If we consider only the lengths of the bars, how many times of the sales of company B is equal to that of company A?
(b) Redraw a bar chart in the figure below to represent precisely the actual situation.
[A copy of the figure is provided in the Appendix.]
(c) Do you think the advertisement of company A is misleading? Explain briefly.
5. Mike uses the following diagrams to point out that Kim spends huge amount of money on transportation. Do you think the amount spent by Kim on transportation must be more than that spent by Mike? Explain briefly.
6. Fast food shop A uses the following diagram to promote its popularity. Do you think fast food shop A must be the most popular among all local fast food shops? Explain briefly.
7. (a) Driving school A uses the following diagram to point out that many of their students passed the driving test last month. Do you think the passing rate of driving school A must be twice the rate of driving school B? Explain briefly.
(b) The figure shows the number of students joining the driving test last month.
(i) Find the passing rate of the students of each driving school in the driving test last month.
(ii) Do you think the accompanying statement of the diagram in (a) is misleading? Explain briefly.
8. Eva uses the following diagram to compare her Mathematics test scores with three classmates’.
(a) Do you think the score of Eva in the second Mathematics test must be the highest among the four students? Explain briefly.
(b) It is given that the scores of the four students in the first Mathematics test are as follows:
Student / Stephen / Eva / Gary / HelenScore / 55 / 40 / 60 / 50
(i) Find the score of each student in the second Mathematics test.
(ii) Is the score of Eva the highest among the four students in the second Mathematics test?
9. The mean, median and mode of a set of data are 8, 10 and 6 respectively.
(a) If 2 is added to each datum, find the new mean, median and mode.
(b) If each datum is multiplied by 5, find the new mean, median and mode.
10. (a) Find the mean, median and mode of 1,2, 2,2,3,3,4,5.
(b) (i) If 8 is added to each datum in (a), find the new mean, median and mode.
(ii) If 5 is subtracted from each datum in (a), find the new mean, median and mode.
11. (a) Find the mean, median and mode of 22, 25,25,25,27,27,29,30,42.
(b) (i) If each datum in (a) is multiplied by 3, find the new mean, median and mode.
(ii) If each datum in (a) is divided by 2, find the new mean, median and mode.
12. The mean, median and mode of the ages of a group of students are 15, 16 and 13 respectively. Find the mean, median and mode of the ages of these students three years ago.
13. The cumulative frequency polygon shows the marks of S3A students in the Mathematics test.
(a) Find the median of the test marks.
(b) The full marks of the Mathematics test are 25. If the full marks are adjusted to 100 by multiplication, find the median of the test marks after the adjustment.
14. The table shows the monthly salaries of 20 employees in a company.
Monthly salary($) / 6000 / 8000 / 10000 / 12000 / 15000 / 20000Frequency / 7 / 5 / 3 / 2 / 2 / 1
(a) Find the mean, median and mode of the monthly salaries.
(b) If the monthly salary of each employee increases by $500, find the mean, median and mode of the monthly salaries after the increase.
(c) If the monthly salary of each employee decreases by 10%, find the mean, median and mode of the monthly salaries after the decrease.
15. The following shows the time spent (in min) by Zoe in jogging over the past 6 days.
40,35,30,25,30,50
It is given that the mean, median and mode of the jogging time are 35min, 32.5min and 30min respectively. If Zoe does not go jogging today, find the mean, median and mode of the jogging time over these 7 days. What will be the changes in these averages?
16. The following shows the heights of 10 students.
155cm,158cm,163cm,168cm,154cm,170cm,177cm,162cm,165cm,163cm
It is given that the mean, median and mode of these heights are 163.5cm, 163cm and 163cm respectively. If the height of the tallest student is not considered, find the mean, median and mode of the remaining heights. What will be the changes in these averages?
17. Given that the mean, median and mode of 10,13,19,22,25,25,28,28,28 are 22, 25 and 28 respectively, find the mean, median and mode of the following sets of data.
(a) 6,9,15,18,21,21,24,24,24
(b) 2,3,5,6,7,7,8,8,8
18. Emily is going to buy some canned drinks from a grocery store, where the mean, median and mode of the selling prices of the drinks are $6, $5.5 and $5 respectively.
(a) If all drinks are sold at a discount of 20%, find the mean, median and mode of the drinks bought.
(b) If Emily is going to buy one less can of drink and its selling price is $6, how will this affect the mean, median and mode of the selling prices of the drinks bought? Explain briefly.
19. There are a total of 10 lessons in a Putonghua course and the mean of the number of absentees in the first 9 lessons of the course is 3. If no student is absent in the last lesson, how will this affect the mean of the number of absentees in each lesson? Verify your answer by finding the mean of the number of absentees in these 10 lessons.
20. The stem-and-leaf diagram shows the monthly sales volumes made by a salesman last year.
(a) Find the mean, median and mode of the monthly sales volumes last year.
(b) It is known that the salesman could get a commission of $250 for each item sold.
(i) Find the mean, median and mode of the monthly commissions last year.
(ii) The monthly income of the salesman is the sum of the basic monthly salary and the commission. If the basic monthly salary of the salesman was $4000 last year, find the mean, median and mode of his monthly incomes last year.
21. The scores of 10 students in a test are as follows:
40,50,50,50,50,90,90,90,90,100
(a) Find the mean, median and mode of the above data.
(b) Which of the averages can best reflect the central tendency of the above data? Explain briefly.
22. The table shows the monthly savings of Padi last year.
Savings($) / 3000 / 3500 / 4500 / 5000 / 5500 / 6000 / 25000Frequency / 3 / 2 / 2 / 1 / 2 / 1 / 1
(a) Find the mean, median and mode of the above data.
(b) Which of the averages can best reflect the central tendency of the above data? Explain briefly.
23. The following shows the time spent (in min) by Kyra in surfing the internet each day last week.
270,260,230,290,0, 240,320
Kyra claims that she spent less than 4 hours in surfing the internet each day last week.
(a) What kind of average does Kyra use to describe the time spent by her in surfing the internet last week?
(b) Do you think the average used by Kyra can reflect the time spent by her in surfing the internet last week? Explain briefly.
(c) Which of the averages can best reflect the time spent by Kyra in surfing the internet last week? Explain briefly.
24. The table shows the number of misprints in each page of a book.
Number of misprints / 0 / 1 / 2 / 3 / 4Frequency / 20 / 17 / 10 / 9 / 8
Matthew claims that there are very few misprints in this book since there are no misprints in most pages.
(a) What kind of average does Matthew use to describe the number of misprints in each page of this book?
(b) Do you think the average used by Matthew can reflect the number of misprints in each page of this book? Explain briefly.
(c) Choose an appropriate average to describe the number of misprints in each page of this book. Give a reason for your choice.
25. After joining a slimming course, 18 out of 40 members have reduced their weights. The reductions in weight are as follows:
Reduction in weight(kg) / 1 / 2 / 3 / 4 / 5Frequency / 9 / 4 / 2 / 2 / 1
The slimming club claims that the average reduction in weight of the members after joining the slimming course
Do you think this claim is misleading? Explain briefly.
26. A restaurant provided 3 kinds of breakfast sets last month, where their mean selling price was $20. This month, the restaurant provided 2 more kinds of breakfast sets. The restaurant adjusted the selling prices of the original breakfast sets, but claimed that the mean selling price of the breakfast sets remained unchanged. It is given that the selling prices of each kind of breakfast set provided in the restaurant are as follows:
Breakfast set / A / B / C / D / ESelling price last month / $18 / $20 / $22 / Not applicable / Not applicable
Selling price this month / $23 / $25 / $27 / $12 / $13
(a) Consider only the breakfast sets available in both months, find the percentage change in the mean selling price.
(b) Do you think the restaurant is trying to mislead the customers? Explain briefly.
27. In a general knowledge competition, the total score of each team is the sum of its scores in each round. The table shows the score of team A in each round.
1st round / 2nd round / 3rd roundScore / 200 / 100 / 400
It is given that the scores of team B in the 1st and 2nd rounds are higher than those of team A by 50% and 100% respectively, while the score in the 3rd round is lower than that of team A by 75%. Yendy claims that on average, the score of team B in each round is higher than that of team A by , i.e. 25%, and thus team B performs better than team A in general.
(a) (i) Find the total score of each team.
(ii) Which team has a higher total score? By what percentage is its total score higher than that of the other team?
(b) Do you agree with the claim of Yendy? Explain briefly.
28. There are 10 families in village A and village B each. The following tables show the number of members in each family and their corresponding water consumption last year.
Village AWater consumption (m3) / 402 / 312 / 278 / 315 / 411 / 368 / 327 / 290 / 324 / 356
Number of members / 3 / 3 / 2 / 4 / 3 / 2 / 3 / 4 / 4 / 3
Village B
Water consumption (m3) / 423 / 415 / 324 / 398 / 402 / 453 / 452 / 390 / 450 / 317
Number of members / 5 / 4 / 3 / 4 / 4 / 5 / 4 / 3 / 4 / 3
The residents of village A claim that the mean of water consumption of each family in village A is 338.3m3 while that in village B is 402.4m3. Therefore, the residents of village B are using too much water and they should therefore reduce their water consumption.
(a) Find the mean of water consumption per resident in each village. (Give your answers correct to the nearest m3.)
(b) Do you agree with the claim of the residents of village A? Explain briefly.
29. The table shows the scores of Stephanie in the Physical Education examination in terms of four areas.
Area / Volleyball / Dancing / Written test / Fitness testScore / 68 / 76 / 80 / 64
Weight / 3 / 2 / 2 / 1
(a) According to the above information, which area is the most important?
(b) Find the weighted mean score of Stephanie.
30. The table shows the scores of Julian in different papers of an examination.
Paper / I / II / III / IV / V / VIScore / 40 / 48 / 72 / 80 / 96 / 60
Weight / 30% / 25% / 20% / 15% / 5% / 5%
(a) According to the above information, which paper is the most important?
(b) Find the weighted mean score of Julian.
31. The table shows the scores of Ricky and Bonnie in Mathematics.