Statistics

ppr maths nbk CHAPTER 6: STATISTICS EXERCISE 1 (Paper 1) 1. Given that the class interval of a set of data is 6 – 9, 10 – 13, 14 – 17, ….. . Determine the upper boundary of the class interval 10 – 13.

Answer:………………….. 2. Calculate the size of class interval 36 – 40. Answer:…………………….. 3. Calculate the mean for the following data 10 21

9 4

4 32

30 27

30 13

29 10

5 2

8 18

11 6

18 26

Answer:…………………….. Questions 4 and 5 are based on the table 1. Table 1 is the frequency table which shows the marks obtained by 10 students in Mathematics quiz. Mark Frequency

1–5 5

6 – 10 4 Table 1

11- 15 0

16 – 20 1

4. Determine the modal class of the data. Answer:……………………..

5. Calculate the mean of the data. Answer:……………………..

6. Given that the mean of a set of data 8, 10, 7, x, 5, 5 is 6.5. Calculate the median of the same set data. Answer:……………………..

7. Find the range of the following set of ungrouped data 2.44, 3.69, 2.74, 1.68, 1.1 Answer:……………………..

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ppr maths nbk Questions 8-10 are based on the table 2. 8. Find the range of class interval the following set of grouped data in table 1

Breadth(cm) Frequency

11 - 16 4

17 – 22 23 – 28 7 8 TABLE 2

29 – 34 9

35 - 40 2

Answer:…………………….. 9. Find the modal class of the data.

Answer:……………………..

10. Find the midpoint of the modal class.

Answer:……………………..

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ppr maths nbk CHAPTER 6: STATISTICS EXERCISE 2 1.Given a set of numbers 2,4,3,4,5,6,8,x,5. Find the value of x if the (a ) median is 4 (b) mean is 5

Answer: (a)……………………………….(b)…………………….

2. The table 1 below shows the scores obtained by a group of students in a quiz competition. Score 1 2 3 4 5 6 Number of 2 3 12 8 3 2 students TABLE 1 Find: (a) the mode (b) the median (c) the mean

Answer: (a)………………..(b)………….…..(c )…………… 3.(a) Complete the following frequency in table 2 Distance (m) Frequency Midpoint 1-3 2 4-6 6 7-9 12 10-12 5 13-15 3 TABLE 2 (b) Based on table 2, calculate the estimated mean distance of the data.

Answer: (a)…………………….(b)…………………………. 4. Find the range of the following set of data (a) 3, 5, 8, 11, 14

(b) 12, 13, 10, 8, 19, 25

Answer: (a)………………………………..(b)……………………………………..

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5.The table 3 below shows the marks obtained by group of students in a Mathematics examination Marks 40 60 75 83 88 Number of 4 6 10 6 x students TABLE 3 (a) If the mean mark is 75, find the value of x. (b) State the minimum value of x if the mode is 88

Answer: (a)………………………(b)………………………………………. 6.

16,25, 13, 26, 15, 16, 18, 17, 20, 24

For the above data, find the (a) range (b) mean Answer: (a)……………………(b)……………………….. 7. Diagram 1 is a pie chart which shows the total number of boys and girls in two clubs. Table 4 shows the number of boys and girls of these clubs, but is incomplete. Clubs Boys Chess 60 Debate (a) Total 100 TABLE 4

Girls 50 (b) (c)

Boys

Girls

1500

DIAGRAM 1

Complete the table.

Answer: (a)…………………..(b)………………..(c)………………………..

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ppr maths nbk 8. Diagram 2 is a pictograph showing the number of blood donors at a blood donation campaign over a period of 3 days.Given that the number of blood donors on Monday make up 30 % of the total blood donors over the period. Monday

Tuesday

Wednesday

Represents 60 blood donors DIAGRAM 2 Calculate (a) the number of blood donors on Wednesday (b) the total number of blood donors the 3 days. Answer: (a)…………………….(b)…………………… 9. Table 5 shows the mass, in kg, of 40 parcels. Mass(kg) Frequency 6-10 4 11-15 10 16-20 7 21-25 10 26-30 5 31-35 4 TABLE 5 . Calculate the: (a) mean mass of the parcels , in kg. (b) midpoint of the third class

Answer: (a)……………………(b)…………………….

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ppr maths nbk 10. Table 6shows the record of overtime done by a group of workers, in hours, in a particular month. Overtime (hours) Frequency 10-19 5 20-29 14 30-39 10 40-49 9 50-59 12 TABLE 6 (a)State the modal class (c) Find the midpoint of the modal class Answer(a)…………………..(b)……………………

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ppr maths nbk CHAPTER 6: STATISTICS DIAGNOSTIC TEST 1. A class interval has an upper limit of 15 and lower limit of 10. The lower boundary is A 9.5 B 10.5 C 14.5 D 15.5 2. The table 1 shows the frequency distribution of the scores of a group of players Score Frequency

1 4

2 3

3 9 TABLE 1 If 3 is the modal score, the maximum value of x is

4 x

5 3

6 2

A 10 B9 C8 D7 3. If the median of a set of integers, 3,8,9,x and 7 is x, the probable value of x is A5 B6 C8 D9 4. The diagram 1 is a pictograph showing the number of durians of different grades sold on a particular day. The information in the pictograph is represented by a pie chart. Grade A durians Grade B durians Grade C durians Represents 50 durians

DIAGRAM 1

Calculate the angle of the sector which represents the number of grade C durians sold. A 900 B 112.50 C 1350 D 157.50

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ppr maths nbk Questions 5 and 6 are based on table 2. Table 2 shows the scores obtained by 12 students. 35 91 74

70 45 46

80 52 53

90 82 88

TABLE 2 5. Find the range of the score A 55 B 56 C 57 D5 6. If x mark is added to each student as a bonus and the mean is 70

1 . 6

Find the value of x. A2 B3 C4 D5 7. Which of the following class interval has a size of 5? A 1.1-1.5 B 2.05-2.10 C 5-9 D 15-20 8 Find the mode for the following data 2, 2, 1, 3, 4, 1, 2 A. 1 B. 2 C. 3 D. 4 9 19, 18, 16, 15, 20, 15, 18, 16 The median for the above set of numbers is A.16 B.17 C 18 D 20

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10 1111 111

The diagram above shows a tally chart. The symbol represents the value A. B. C. D.

5 7 8 13

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ppr maths nbk CHAPTER 6 : STATISTICS EXERCISE 1 ( PAPER 2)

1. The data in Diagram 1 shows the marks obtained by 30 students. By using five class intervals, construct a frequency table for the data. 11 31 35 42 17

24 36 36 14 34

31 25 10 44 35 30 18 18 34 32 DIAGRAM 1

22 28 13 30 20

21 27 35 16 37

2. Complete Table 1 Class

Lower limit

Upper limit

Lower boundary

Upper boundary

Class size

55 – 60 61 – 66 67 – 72 73 - 78 TABLE 1

3. Diagram 2 shows the masses of tomatoes, in kg, yielded by a farm for a period of 30 days. 59 62 36

59 59 71

68 80 74

50 62 51

42 46 60 74 55 56 83 64 44 DIAGRAM 2

57 76 55

71 40 51

47 53 51

(a) Construct a frequency table with class intervals 36 – 43, 44 – 51 and so on and then find the midpoint of each class. (b) State the modal class. (c) Calculate the mean mass of the tomatoes yielded by the farm per day.

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4. The data in Diagram 3 shows the number of papayas sold by Pak Ali per day for a period of 30 days. 25 26 37 31 24 30

45 20 31 40 28 28

42 36 25 32 35 22 30 27 21 33 34 29 DIAGRAM 3

32 38 32 26 39 33

(a) Based on the data in Diagram 3 and by using a class interval of 5, complete Table 2. Class interval 20 – 24 25 – 29

Frequency

Midpoint

TABLE 2

(b) Based on Table 2, calculate the estimated mean number of papayas sold. 24 17 24

10 31 18

36 35 40

19 11 35

19 25 31 32 11 20 DIAGRAM 4

26 15 23

33 33 27

16 27 37

30 38 34

5. The data in Diagram 4 shows the heights, in cm, of 30 seedlings in a nursery. (a) State the range of the data. (b) Based on the data in Diagram 4, complete Table 3. Height (cm)

Frequency

Midpoint

Upper boundary

10 – 16 17 – 23 24 – 30 31 – 37 38 – 44 TABLE 3

(c) Based on Table 3, i) state the modal class ii) calculate the mean height of the seedlings.

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ppr maths nbk CHAPTER 6 : STATISTICS EXERCISE 2

1.

Given a set of numbers 2, 4, 3, 4, 5, 6, 8, x , 5, . Find the value of x if the ( a ) median is 4 ( b ) mean is 5

2.

Table 1 shows the score obtained by a group of students in a quiz competition. Score Number of students

1 2

2 3

3 12

4 8

5 3

6 2

Table 1 Find ( a ) the mode ( b ) the median ( c ) the mean

3. The data below shows the marks obtained by 40 students in a monthly test. 99 70 45 69 55

88 32 89 76 40

75 70 45 88 80

92 58 93 58 80

58 90 61 91 39

75 68 81 67 46

80 50 58 71 61

70 78 65 52 69

(a) Using a class interval of 10 marks , complete the following table.

Mark 21 - 30 31 - 40

Frequency

Midpoint

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(b) For this part of the question, use the graph paper By using a scale of 2 cm to 10 marks on x – axis and 2 cm to 1 student on y – axis , draw a frequency polygon based on the data. ( c ) From your answer in (a), (i) determine the modal class, (ii) calculate the estimated mean of the group of students.

4. The data below shows the mathematics test marks of 40 students. 86 92 85 74 82

98 86 93 75 90

72 93 72 83 91

96 87 84 85 76

94 81 72 88 68

90 80 86 69 96

76 83 86 90 89

80 67 88 79 78

(a) By using the a class interval of 5 marks , complete the following table.

Mark 65 - 69 70 - 74

Frequency

Midpoint

(b) From the table in (a) (i) state the modal class, (ii) calculate the estimated mean mark of test. (c) For this part of the question, use the graph paper. By using a scale 2 cm to 5 marks on x-axis and 2 cm to 1 student on y-axis, draw a histogram for the data.

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5. Mass ( gm )

Frequency

20 - 24

0

25 - 29

8

30 - 34

10

35 - 39

36

40 - 44

48

45 - 49

40

50 - 54

27

55 - 59

11

The table above shows the frequency distribution of mass of books . ( a ) State the midpoint of the modal class ( b ) Based on the table above , construct a cumulative frequency table. ( c ) For this part of the question, use the graph paper. By using a scale of 2 cm to 5 gm on x – axis and 2 cm to 20 books on y – axis , draw an ogive for the data . (d ) From your ogive in ( c ), find i. the interquartile range, ii. the number of books with length greater than 50 cm.

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ppr maths nbk CHAPTER 6 : STATISTICS DIAGNOSTIC TEST

1. Data below shows the number of papaya trees planted by 50 farmers.

60 65 70 68 74

77 71 66 77 80

70 62 64 74 70

81 66 89 63 72

73 78 81 71 75

69 76 61 65 82

79 64 73 87 76

69 71 78 67 81

75 73 73 63 68

67 79 68 74 74

(a) (i) Using size of class interval 5 , complete the Table 1 below.

Class Interval 55 – 59

Upper boundary

Frequency

Cumulative Frequency

Table 1 (ii)

Hence , state the modal class

(b) By using a scale of 2 cm to represent 5 trees on the x – axis and 2 cm to represent 5 farmers on the y – axis , draw an ogive for the data above. (c) Based on the ogive in (b) , Osman make a conclusion that 25% of the farmers planted less than 56 trees. Determine whether the conclusion is correct or not and give a reason.

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2. Encik Shamsudin reared a total of 148 turtles. The distribution of the length of the turtles is shown in Table 2.

Length (cm) 5–9 10 – 14 15 – 19 20 – 24 25 – 29 30 – 34 35 – 39

Frequency 9 19 29 43 30 14 4 Table 2

(a) By stating the answer correct to two significant figures, calculate the mean length of the turtles reared. (b) Construct a cumulative frequency table. By using a scale of 2 cm to represent 5 cm on the x – axis and 2 cm to represent 20 turtles on the y – axis , draw an ogive for the data above (c) From the ogive drawn in (b), find the median, (i) the first quartile, (ii) (iii) the third quartile, (iv) the interquartile range.

3. The closing price, in sen, of the 50 counters traded at Bursa Malaysia on a day is given in Figure below..

200 169 146 250 136

150 196 218 178 258

189 208 154 259 142

175 249 234 198 163

255 124 162 146 186

130 121 241 182 204

214 180 193 201 156

161 155 187 160 245

230 144 254 186 194

217 158 184 183 164

(a) Determine the range of price of the 50 counters.

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(b) Using size of class interval 20 , complete the Table 3 below. Class Interval 121-140

Mid point

Frequency

Table 3 (c) Based on the frequency table constructed in (b) , draw a histogram for a data.

4. The heights, in cm, of 50 plants are distributed as shown in the following table. (a)

Height(cm) 40 – 44 45 – 49 50 – 54 55 – 59 60 – 64 65 – 69 70 – 79

Midpoint

Frequency 3 5 10 16 8 6 2

(i) Copy and complete the above table (ii) Hence , calculate the mean height of the plants. (b) Upper 39.5 Boundary (cm) Cumulative 0 frequency

44.5

(i)

Based on the information from the table in (a) , copy and complete the above table.

(ii)

Using a scale of 2 cm to represent 5 cm on the x – axis , and 2 cm to represent 5 plants on the y-axis, draw an ogive for the distribution. From the ogive , find (a) the median (b) the third quartile

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5. (a) Number of Television sets sold Number of Shops

8

9

10

11

12

13

2

5

8

10

9

6

The above table gives the numbers of televisyen sets sold by 40 electrical shops on a certain day.Find the mode (i) the mean of the distribution. (ii)

(b) Time(minutes) 6.1 – 7 .0 7.1 – 8.0 8.1 – 9.0 9.1 – 10.0 10.1 – 11.0 11.1 – 12.0 12.1 – 13.0 13.1 – 14.0

Number of participants 8 14 22 46 38 20 8 4

Upper boundary

Cumulative Frequency

The above table shows the frequency distribution of the times , in minutes, taken by 160 participants of a jogathon.Copy and complete the table. (c)

Using a scale of 2 cm to represent 1 minute on the x –axis and 2 cm to represent 20 participants on the y-axis, draw an ogive for this distribution. From the ogive , find the median (i) the interquartile range (ii) (iii) the number of prize winners , given that participants who clocked less than 8.0 minutes were given prizes.

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