name: class: s.3 group: s3m chapter 6 measures of central tendency · 2020. 4. 5. · chapter 6...

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Name: Class: S.3____ Group: S3M___ Chapter 6 Measures of Central Tendency

Exercise 6.1 1. Find the mean of each of the following sets of data. (a) 1, 5, 5, 6, 13 (b) –4°C, 1°C, –6°C, –4°C, –1°C, –7°C (c) 32 m, 20 m, 13 m, 17 m, 15 m, 11 m, 18 m

2. The weights of five school bags are 1.8 kg, 2 kg, 2.5 kg, 3.1 kg and 3.6 kg. Find the mean weight of the five school bags.

3. Mabel’s scores in six tests are 60 marks, 64 marks, x marks, 70 marks, 72 marks and 80 marks. If

Mabel’s mean score in the six tests is 69 marks, find the value of x. 4. Find the median of each of the following sets of data. (a) 1, 4, 2, 1, 7 (b) 20, 29, 26, 22, 21, 23 (c) 0.5 L, 0.1 L, 0.7 L, 1.3 L, 1.1 L, 0.9 L, 1.5 L

5. The ages of five teachers are 50, 32, 22, 41 and 44. Find the median age of the teachers. 6. Find the mode of each of following sets of data. (a) 1, 1, 3, 1, 4, 7, 6, 5 (b) –7, –3, –2, –1, –3, –2, –1, –3 (c) $5.1, $2.4, $3.4, $2.8, $3.9

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Exercise 6.2 1. 40 households are interviewed about the numbers of computers they have. The results are shown in the

table below. Number of computers 0 1 2 3 Frequency 4 15 12 9

Find the mean number of computers the households have.

2. The table below shows the numbers of days of sick leave that the staff of a company took in a certain month. Number of days 0 1 2 3 4 5 Frequency 11 7 4 3 2 1

Find the median number of days of sick leave that the staff took.

3. The table below shows the numbers of patients in a clinic per hour. Number of patients 0 1 2 3 4 5 Frequency 2 2 2 1 3 0

Find the mode of the numbers of patients in the clinic per hour.

4. The table below shows the thickness (in mm) of the books on a bookshelf. Thickness of books (mm) 1 – 5 6 – 10 11 – 15 16 – 20 Class mark (mm) Frequency 28 22 16 14

(a) Complete the above table. (b) Find the mean thickness of the books.

5. The table below shows the numbers of pages in some novels.

Number of pages 1 – 50 51 – 100 101 – 150 151 – 200 Frequency 4 2 9 6

Find the model class of the numbers of pages in the novels.


Exercise 6.3 1. The following table shows Kate’s results (in marks) and the weight of each paper in a mathematics

examination. Paper 1 Paper 2 Score (marks) 70 90 Weight 65% 35%

Find Kate’s weighted mean score in the mathematics examination.

2. In a job interview, the manager of a company assesses the performance of an applicant based on his / her qualifications, experience and communication skills. The table below shows the scores (in marks) of an applicant, Paul, in the three areas and the weight of each area. Qualifications Experience Communication skills Score (marks) 62 50 70 Weight 40% 30% 30%

If the score of an applicant is more than 60 marks, the applicant will be called for a second interview. Will Paul be called for a second interview?

3. The table below shows Joanna’s results in the four assessments of the subject ‘Life and society’ and the weight of each assessment. Newspaper

cuttings Group

discussion Presentation Written report

Score (marks) y 64 55 88 Weight 12% 16% 30% 42%

If Joanna’s weighted mean score is 72.1 marks, find the value of y. 4. The stock price index of a city is the weighted mean of the price indices of five different stocks A, B, C,

D and E. The table below shows the price indices of the stocks. Stock A Stock B Stock C Stock D Stock E Price index 98 110 135 106 102

If the weights of stocks A, B, C, D and E are 1, 2, 1, 4 and 2 respectively, find the stock price index.


Exercise 6.5 1. For a set of data, the mean is 6, the median is 9 and the mode is 4. Find the new mean, the new median

and the new mode when each datum of the set of data (a) is increased by 1, (b) is decreased by 3. 2. For a set of data, the mean is 12, the median is 6 and the mode is 24. Find the new mean, the new

median and the new mode when each datum of the set of data (a) is multiplied by 5, (b) is divided by 6. 3. (a) Find the mean, the median and the mode of the set of data 2, 2, 2, 3, 3, 4, 4, 5, 5, 8, 10, 12. (b) Using the results of (a), find the mean, the median and the mode of the set of data 6, 6, 6, 9, 9, 12,

12, 15, 15, 24, 30, 36.


Chapter 7 Percentages (II) Exercise 7.1 1. Find the percentage change when 120 changes to 150. 2. When 1100 decreases by 8%, find the new value. 3. When a number decreases by 20%, it becomes 180. Find the original number. 4. Find the final value after 30 increases by 20% and then increases by 10%. 5. The original price of a tablet computer was $4500. Its price decreased by 4% one month after the first

launch, and then further decreased by 5% in the following month. Find the new price of the tablet computer.

6. A number increases by 18% and then decreases by 10%. If the resulting number is 8496, find the

original number. 7. The income and the expenditure of a company were $1 200 000 and $750 000 respectively last year.

This year, the income and the expenditure of the company increase by 15% and 20% respectively. Find the profit of the company this year.


Exercise 7.2 1. The present value of a diamond ring is $20 000. If its value increases by 6% each year, what will its

value be after two years? 2. The present value of a gold coin is $5000. If its value increases by 10% each year, what will its value be

after three years? 3. Jason buys an LCD TV for $9800 today. Its value will decrease by 28% each year. Find the value of the

LCD TV after two years. (Give the answer correct to the nearest dollar.) 4. Henry bought a car for $120 000 three years ago. Its value has decreased by 15% each year. Find the

present value of the car. 5. The height of a tree has increased by 25% each year. If the present height of the tree is 18 m, what was

its height two years ago? 6. The value of a TV set decreases at a constant rate of 12% per year. If the present value of the TV set is

$1936, find its value two years ago.


Exercise 7.3 1. A sum of $1000 is deposited at an interest rate of 4% p.a. for 3 years, compounded yearly. Find the

amount and the interest. 2. A sum of $5000 is deposited at an interest rate of 7% p.a. for 5 years, compounded yearly. Find the

amount and the interest. 3. Tammy deposits $30 000 in a bank at an interest rate of 7% p.a. for 2 years, compounded half-yearly.

Find the amount. 4. A sum of $8000 is deposited at an interest rate of 4% p.a. for 2 years, compounded quarterly. Find the

amount. 5. A sum of $10 000 is deposited at an interest rate of 8% p.a. for 1 year, compounded monthly. Find the

amount and the interest. 6. Joyce deposits $P in a bank for 3 years and the interest rate is 5% p.a., compounded yearly. If the

amount received is $4630.5, find the value of P.


Chapter 8 Quadrilaterals In each of the following, ABCD is a parallelogram. Find the unknown(s). (1 – 4) 1. 2. AEC and BED are straight lines.

3. 4.

5. In the figure, ABCD is a parallelogram. BCF and CDE are straight lines. Find the values of x and y.

In each of the following, ABCD is a rhombus. Find the values of x and y. (6 – 8) 6. AC and BD intersect at E. 7. 8. AC and BD intersect at E.


In each of the following, ABCD is a rectangle. Find the values of x and y. (9 – 11) 9. 10. 11. AC and BD intersect at E.

In each of the following, ABCD is a square. Find the values of x and y. (12 – 14) 12. 13. AC and BD intersect at E. 14. AFD, FEC and BED are straight lines.

15. In the figure, PQRS is a rhombus. PR and QS intersect at T. ÐTQR = 40°. Find the values of x, y and z.

16. In the figure, ABCD is a rectangle. AC and BD intersect at E. ÐEBC = 30°. Find the values of x and y.

13. In the figure, ABCD is a rectangle. E is a point on AD such that ÐCEB = 55° and ÐDCE = 20°. Find

ÐABE.

name: class: s.3 group: s3m chapter 6 measures of central tendency · 2020. 4. 5. · chapter 6...

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