STATISTICS

1. The stem-and-leaf diagram below shows the instantaneous speed of some vehicles at a road junction.

StemLeaf

3 5 6 8

4 4 5 5 8 9

5 0 8 8 9

6 1 2 2 8 8

7 0 0 0 9 9

8 0 0 5 8

Key: 3 | 5 represents 35 km/h

(a) Complete the grouped frequency table below. [3]

Speed (km/h)Mid-valueFrequency

30 3934.53

40 49

50 59

60 6964.55

70 7974.5

80 894

(b) State the class interval that the median lies in. (c) Find the percentage of vehicles that were speeding, given that the speed limit of a vehicle at the road junction is 70 km/h. Give your answer correct to 1 decimal place. (d) Using the data from the table, calculate the mean speed of vehicles. Give your answer correct to 3 significant figures.

Answer:(b)____________________[1]

(c)_________________ %[2]

(d)_______________ km/h[2]

2.The time in minutes taken by 20 patrons at a food court to finish their meal is represented by the dot diagram below.

(a)Find the mean, median and mode of the data.[4]

(b)The management of the food court says that the average time taken by a patron to finish a meal is 15 minutes. Does your data prove or disprove this statement? Explain briefly. [1]

3.Number of marks obtained11 2021 - 3031 - 4041 - 5051 6061 - 7071 - 8081 90

Number of students2410182220168

The table shows the results of an English test taken by 100 students.

(a)Complete the table below.

Number of marks obtainedMid-value (x)Frequency (f)fx

11 - 20

21 30

31 40

41 50

51 60

61 70

71 80

81 90

Total

[3]

(b)Find the mean score.

Answer(b)........... marks[1]

4.The table below shows the number of printers owned by each of the 15 companies.23501

10221

13413

1. Draw a dot diagram to represent the information given.

1. Find the median number of printers.

[2]

[1]

5.

The Stem-and-leaf diagram below shows the prices of gift sets available in a shop.

Stemandleaf diagram for the prices of gift sets

StemLeaf

23 4 5

30 0 1 3 5

42 2 6 7

50 3 9

Key: 2|3 means $23

(a) Find the mean of the distribution.

(b) Find the median of the distribution.

(c) Find the percentage of gift sets with prices more than $50.

[2]

[1]

[1]

6.The stem and leaf diagram below shows the prices of some handphone covers. Stem leaf1. 3 6 61. 1 3 5 5 55 0 2 key 2|3 represents $23

1. Find the median price.

1. Find the mean price.

Answer (a) $..............................[1]

(b) $ .............................[2]

7.The stem and leaf diagram below shows the height of 14 students in the class.(a)Find the median height of the students.(b) Find the modal height of the students.

.

Ans:(a) _________________cm [1]

(b) _________________cm [1]

8.In a survey, 12 children were asked the number of siblings that they have.

The results are 0, 1, 2, 3, 2, 0, 0, 1, 0, 1, 0, 4

1. Complete the dot diagram below:

[1]

1. Express the total number of children who have at least 2 siblings as a fraction of the total number of children. Given your answer in its lowest terms.

1. The same information is to be shown in a pie chart. Find the angle which represents the children who have 1 sibling.

Answer (b)................................[1]

(c)............................. [2]

9.The weight of a group of children in kg are 35, 38, 45, 47, 35, 39, 35, 43, 45, 42. Calculate:(a) the mean,(b) the modal,(c) the median weight of the children.

Ans: (a) __________________kg [1]

(b) __________________kg [1]

(c) __________________kg [1]

10. A gardener decided to sow 5 seeds in 100 pots. The number of seeds germinating in each pot was recorded and the results were given below.No of seeds germinating

012345

No of pots

1030x20y5

1. Find x and y if the value of the mean is 2.05.(b)Find the smallest possible value of x if the median is 3.

Ans: (a) x = ________________ y = ________________ [3](b) ___________________ [2]11.The distance in km travelled by 20 adults to their place of work is recorded in a stem-and-leaf diagram shown below.

StemLeaf

068

112227899

23779

302558

41

(a) Write down the modal distance travelled.

(b) Find the median distance travelled.

Ans :(a)_________________ km [1]

(b)_________________ km [1]

12.Some children were asked how many television programmes they hadwatched on the previous day. The table shows the results.

Number of programmes watched0123

Number of children793x

(a)Write down the largest possible value of x given that the mode is 1. (b)Calculate the value of x given that the mean is 1. (c)Hence, find the median.

Ans :(a)x = _________________ [1]

(b)x = _________________ [2]

(c)Median = ____________ [1]

13.The mass, in grams, of 30 apples were measured and recorded below.

154162158172166181

170124134162155166

144174157165162156

163162164162171153

126163133161158162

(a)i.Use the information above and complete the table below. ii.Hence find the mean mass of the apples. (b)State the modal mass range of the apples

(b) i.Mass / gMid-value (x)Frequency (f)fx

120 < x 130125

130 < x 140135

140 < x 150145

150 < x 16015571085

160 < x 170165

170 < x 180175

180 < x 190185

= 30x =

[2]

Ans: (a) mean = ______________ g[2](b) modal mass range = _______________ g [1]

14.A survey of the number of books read by a group of primary school pupils in a year is displayed in the stem-and-leaf diagram below.

Stem-and-leaf diagram of the number of books read by pupils in a yearKey: 04 means 4 books.

StemLeaf

044568

113357899

25889

3002558

4234

(i)How many pupils participated in the survey?

[1]

(ii)Calculate the percentage of pupils who read at least 13 books but not more than 28 books in a year.

[2]

(iii)One of the pupils data is omitted accidentally by the surveyor. When the pupils data is included, the mean number of books read is 23. Find the number of books read by this pupil.

[2]

15.In another survey, the number of books read by a group of secondary school pupils during the end of year holidays is tabulated below.

No. of books read 01234567

Frequency 3528x102

Given that x is a positive integer, find

(i)the value of x if the median number of books read is 3.5. [2]

(ii)the maximum value of x if the modal number of books read is 3. [1]

(iii)the value of x if the mean number of books read is 2.72. [2]

16. The table below shows the marks of a science test scored by a group of students.Marks232425262728

Number of students01445x3

Find (a)the smallest possible value of x if the modal mark is 27.(b)the largest possible value of x if the median is 25.

Answer: (a) x =____________________ [1]

(b) x =___________________ [1]

17.The stem and leaf diagram below shows the marks scored by 30 students in aScience test.

StemLeaf

51 6 6 8

60 0 2 3 4 4 5 6 6 7 7 8 8 8 9

71 1 2 4 5 6 6 7

82 3 5

Key: 76 represents 76 marks.

(a)Find the(i)mean,[2](ii)median,[1](iii)mode of the distribution.[1]

(b)What is the percentage of students who scored more than 75 marks?[1]

18. The time taken in minutes to travel from Orchard Road to Suntec City by taxis are recorded as shown below:

12 8 65 11 6 6 42 8 5 90 12 9 8 14 11 (a) Construct a stem and leaf diagram to represent the time taken of the taxis. (b) Find the modal time taken of the taxis, (c) Find the median time taken, (d) Find the mean time taken by each taxi, (e) The mean and the median time taken can be used to represent the data. Which is a better choice? Explain. StemLeave

(a) [1]

19.The distance travelled by 400 students from their home to the school is given in the table below.

Distance x in km0< x 5 5< x 10 10< x 15 15< x 20 20< x 25

No. of students100120708030

(a) Write down the modal class. [1] (b) Calculate an estimate of the mean distance travelled by the 400 students. [2]

21a. The table below shows the number of hours spent on computer games by a class of 40 students. Hours12345

Number of pupils6x116y

(i) Show that x + y = 17 . [1] (ii) If the mean of the distribution is 2.8, show that 2x + 5y = 49. [2] (iii) Hence, find the value of x and of y.[3]

b.Another class of students took the same survey. The results are shown in the table below.

Hours12345

Number of pupils599m4

(i) State an inequality for the value of m such that the mode is 4.[1](ii) Given that the median is 3, find the maximum value of m.[1]

22.The weights of 100 men are recorded in the table below.

(a)Mass (kg)Frequency

3

10

22

34

20

11

Calculate the estimated mean weight of the 100 men.

[2]

(b)The stem and leaf diagram shows the distribution of the PSLE scores obtained by class 6C in ABC Primary School.

StemLeaf

181 155889

1923334489

200588

21015588

2213469

Key: 18 | 1 means 181 points

(i) Find the mean, median and mode of the distribution.

[3]

(ii) Given that 20% of the students did not qualify for the Express stream, find the least score needed to qualify for the Express stream.[2]

23.The stem-and-leaf diagram below represents the test marks of 24 pupils.(a)What is the mode mark?(b)What is the median mark?

StemLeaf

4578

5556

62233345578

712678

8028

Key: 4|5 means 45 marks

Answer:(a) marks[1](b) marks[1]

24.The height, in centimeters, of 15 primary six pupils are measured and shown below.

1181231961581291271431391451591391391481.13116

(a)One of the measurements is recorded in metres. Identify the measurement and rewrite it in centimetres.[1](b)The height of another pupil is measured wrongly by an additional 50 cm. Identify the wrong measurement and write down the correct measurement in centimetres.[1](c)Using the correct measurements, find the mean height correct to the nearestcentimetre.[2](d)Copy and complete the frequency table below.[2]Height (x cm)Frequency

(e)Use the frequency table to find the mean height correct to the nearest centimetre.[2](f)Give a reason for the difference in your answer in (c) and (e).[2]

25.

The dot diagram shows the results of a survey on the sale of shoes of a branded design, Queenie,of various sizes. 5 6 7 8 9 Shoe Size

(a) What percentage of the sales goes to shoes of sizes from 6 to 8? ( Correct answer to 3 sig fig)

(b) A store keeper stocked up the following shoes for sale.Shoe SizeNo. of shoe in stock

520

650

725

835

910

State, with a reason, shoe of which size will be sold out first, based on the survey.

Answer: (a) ____________________ [1]

(b) Shoe of Size _______ will

be sold out first because ______________________________________ ________________________________________________________ [2]

26. A class of 33 students was given a task to cut 100 pieces of stars within 3 hours. The number of stars that they cut is listed below. 89 78 56 43 92 95 24 72 58 65 55

98 81 72 61 44 48 76 82 91 76 81

74 82 99 21 34 79 64 78 81 73 69

(a) Complete the stem and leaf diagram below. The first line of the above figures has already been filled in.[1]

1

24

3

43

5685

65

782

89

925

(b) Complete the ordered stem and leaf diagram below for the 33 students.[1]1

2

3

4

5

6

7

8

9

(c) Find the median number of stars cut.

Answer: (c) _____________________[2]

27. There are 15 people in a company. Nine office workers are each paid $2 500. Six managers are paid $5500, $6 500, $6 800, $7 000, $7 200 and $10 000 each.(a) (i) State the median salary. (ii) State the mode of this distribution. (iii) Calculate the mean salary, correct to the nearest cents. (b) Explain why the mean is not a good average to use for the above distribution. Give a reason for your answer.(c) One person is chosen at random from the people working in the company. Calculate the probability that the chosen person is a manager.

Answer (a) (i)$___________________[1]

(ii) $ _________________ [1]

(iii) $ ________________ [2] (b) Reason ______________________________________________

_____________________________________________________ [1]

(c) ___________________ [2]28.Some students were asked how many hours they had spent on the Internet for the previous day. The table below shows the results.

Number of hours spent0123

Number of students7103x

a) Write down the largest possible value of x given that the mode is 1.b) Calculate the value of x given that the mean is 1.c) Write down the largest possible value of x given that the median is 1.

Ans: a) ________________ [1] b) ________________ [2]c) ________________ [1]

29.A survey was done on a group of 30 students on the amount of time (in minutes) they spent doing their homework per day.

80100801107595

85701251108590

110958075150115

9513010010075145

9575120809585

[3][2]

[2]

a) Represent the above data using a stem-and-leaf diagram.b) Hence, find the median time of the distribution.c) If a pupil is picked at random from the group, find the probability that the pupil spent 80 minutes revising his work per day.

30. (a)The frequency table shows the number of goals scored in a series of soccer matches.

Number of goals012345

Number of matches357x20

(i)If the mode is 2, find the largest value of x. (ii)If the median is 2, find the smallest possible value of x. (b)A class of 24 students took a Mathematics test. Their scores are represented in the stem and leaf diagram as shown.StemLeaf

02 9

12 4 8

20 1 2 6 7 7 7 8 9 9

30 1 4 5 7 9 9

40 2

Key: 1 | 4 means 14 marks(i)For the whole class, find the median score.(ii)A new student later joined the class and sat for the same test. If the mean score of the class became 28, find the score of the new student.

Answer (ai) ______________________________ [1] (aii) ______________________________ [1]

(bi) _____________________________ [1]

(bii) _____________________________ [2]