statitics

Matematics Form 4

4. Skill Practice1. clone SPM 2005The data in diagram below show the marks of a Mathematics test for 36 pupils

754647486654514531723560433563564152

334953807343574441546360456758624559(a) Compete the table below by using data above and a class interval of 8 marks.MarksMidpointFrequency

29 - 36

37 - 44

45 - 52

53 - 60

61 - 68

69 - 76

77 - 85

(b) Based on your table in (a)(i) state the modal class

(ii) calculate the mean mark of the Mathematical test and give your answer correct to 2 decimal places.

(iii) By using a scale of 2 cm to 8 marks on the horizontal axis and 2 cm to 1 pupil on the verticals axis, draw a histogram for the data.2. The table frequency table below shows the scores, the number of correct answers of 92 pupils of Form 4 in an objective test paper.ScoreNumber of student

1 88

9 1626

17-2436

25 3214

33 - 408

(a) Complete the table below

ScoreFrequencyCumulative

FrequencyUpper boundary

(b) By using a scale of 1 cm to 8 correct answers on the x-axis and 1 cm to 20 pupils on the y-axis, draw an ogive(c) Use your ogive to find

(i) the median score

(ii) interquartile range

(d) 18 pupils are given an A grade for the paper, determine the minimum score to qualify for grade A.

12. The frequency table below shows the marks obtained by 120 pupils in a test.

MarkNumber of students

1 104

11 209

21 3020

31 4038

41 5025

51 6016

61 708

(a) Find the range of the mark

(b) Complete the table below

MarkFrequencyCumulative


(c) Using a scale of 2 cm to 10 marks on the x-axis and 2 cm to 20 pupils on y-axis, draw an ogive.(d) Use your ogive to determine

(i) first quartile

(ii) third quartile

(iii) interquartile range

(e) If the passing percentage is 85 % , determine the passing mark.

13. Data below shows the result of an IQ test ( Intelligence Quotient) of 36 students.

102120123125112126

118114126123118120

126124127121120119 108128105131 123 113

118120124106130 120 125 126118117124104

(a) Determine the range of IQ

(b) Complete the frequency table below

IQfrequencyLower

boundaryUpper boundary

100 - 104

(c) Construct a histogram for the data

(d) Draw a frequency polygon on the histogram..

(e) Estimate the mean IQ of the students.

14.Diagram below is an ogive which shows the result of a survey on total working hours in a day of a group of teachers.(a) Find the number of teacher who took part in the survey.(b) Find the number of teacher who worked more than 10 hours a day.(c) Find the number of teachers who has a total daily working hours between 9 to 12 hours. 15. Data below shows the total prep hours in a week of 30 Form 4 students.

627131521249162419283021182018193010824273128231614283021

(a) Complete the table below with the data above.Time

(Hour)FrequencyCumulative

frequencyUpper

Boundary

29-32

(b) By using a scale of 2 cm to 4 hours on x-axis and 2 cm to 5 students on the y-axis, draw an ogive.(c) Calculate the percentage of students who spent more than 22.5 hours on prep.(d) It is found that 30 % of the students do not have sufficient prep in a week. Determine the minimum required hours of prep.Answer To Skill Practice

1(a)MarksMidpointFrequency

29 - 3632.54

37 - 4440.55

45 - 5248.59

53 - 6056.59

61 - 6864.55

69 - 7672.53

77 - 8580.51

(c) (i) 45 52 marks

(ii) 52.72 marks

2. (a)

ScoreFrequencyCumulative


-7 0000.5

1 8888.5

9 16263416.5

17-24367024.5

25-32148432.5

33-4089240.5

(b)

(c) (i) median = 19.7 (ii) 23.7- 12.5 = 11.2

(d) 27

3. (a) Range = 65.5 5.5 = 60

(b)

MarkFrequencyCumulative


-9 - 0000.5

1 104410.5

11 2091320.5

21 30203330.5

31 40387140.5

41 50259650.5

51 601611260.5

61 70812070.5

(c)

(d) (i) K1 = 29.5 marks

(ii) K3 = 47.5 marks

(iii) interquartile range = K3 K1 = 18 marks

(e) 85 % passes = 15 % failure

Cummulative frequency at 18 , corresponding mark= 24 marks

4. (a) range = 131 102 = 29

(b)

IQfrequencyLower

boundaryUpper boundary

100 - 104299.5104.5

105 1093104.5109.5

110 1143109.5114.5

115 1196114.5119.5

120 12412119.5124.5

125 1298124.5129.5

130 1342129.5134.5

(c) , (d)

5. (a) 32 teachers (b) 28 teachers

(c) 24 -2 = 22 teacher

15.

(a)

Time

(Hour)FrequencyCumulative

frequencyUpper

Boundary

1 4004.5

5 - 8228.5

9 122412.5

13 - 165916.5

17 2051420.5

21 2472124.5

25 2852628.5

29 - 3243032.5

(b)

(c)Percentage =( (30-17)/30) X 100 = 43.33 %

(d) (30/100) x 30 = 9 student 16.5 hour

9.5

10.5

11.5

13.5

12.5

14.5

4

8

12

16

20

24

28

32

Number of teacher

Working hour ( Hr)

8.5

15.5

28.5

36.5

44.5

52.5

60.5

68.5

76.5

85.5

Frequency

Marks

2

4

6

8

10

0.5

8.5

16.5

24.5

32.5

40.5

0.5

10.5

20.5

30.5

40.5

50.5

60.5

70.5

20

40

60

80

100

0

120

Cumulative frequency

Mark

Frequency

Frequency

94.5 99.5 104.5 109.5 114.5 119.5 124.5 129.5 134.5 139.5

4.5 8.5 12.5 16.5 20.5 24.5 28.5 32.5

5

10

15

20

25

30

Cumulative frequency

Prep Hour (Hour)

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