STATISTICS

 KELANTAN PAPER 1 2019

9 Table 1 shows the scores obtained by a group of students in a competition.

Score Number of students

0 5

1 q

2 6

3 4

4 7

Table 1

Find
a) the maximum value of q if the mode is 4,
b) the range of values of q if the median is 2

 KELANTAN PAPER 2 2019

9 Table 2 shows the masses of a group of students.

Mass (kg) 20 - 24 25 - 29 30 - 34 35 - 39 40 - 44

Number of students 10 22 29 p 15

Table 2

Given the mean mass of the students is 32.6 kg.

Find
a) the value of p,
b) the variance, of the distribution,
c) interquartile range, without using an ogive.

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 NEGERI SEMBILAN PAPER 1 2019

16 Data below shows the scores of seven athletes in a sport tournament.

101, 98, 96, 97, 103, 96, 99

a) What is the best measure of central tendency to represent the set of data?
Give your reason.
b) An athlete whose score is 97 decided to withdraw from the tournament and he was
replaced with another athlete whose score is 210.
What is the best measure of central tendency to represent the new set of data?
Give your reason.

 NEGERI SEMBILAN PAPER 2 2019

4 Table 1 shows the score of 7 students in a quiz arranged in increasing order.

Student Shara Zahidah Masitah Naliza Wafi Lutfi Ben

Score 6 ? 8 ? 13 15 18

Table 1

a) Given the interquartile range of the score is 7 and the mean score is 11, find the
score of Zahidah and Naliza.
b) Find the standard deviation of the score.
c) The students sat for another written quiz and each of them managed to double their
score. State the new mean and the new variance.

 PERLIS PAPER 1 2019

2
1 A set of data consists of 8, 2, 7, x - 2, 5 and 4. Given the mean is 5.5, find
a) the positive value of x,
b) the median using the value of x in (a).

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2 Table 2 below shows the score of three sports houses in a competition.

Sports house Mean Standard deviation

Red 80 4
Blue 65 1
Yellow 50 3

Table 2

a) Which sports house shows the most consistent achievement in the competition?
Give reason for your answer.
b) State the variance for the sports house stated in 2(a).

 PULAU PINANG PAPER 1 2019

10 The mean of s set of twenty five numbers is 24.

a) If each of the number increase by 3 and multiplied 2, find the new mean of the set.
b) If two numbers k and k + 2 are removed from the set, the mean of the new set is 22,
find the value of k.

11 Table 11 shows the mass of each member in Rahim’s family.

Name Rahim Suzy Naqib Anis Zali

Mass (kg) 54.5 69.1 25.4 18.2 7.5

Table 11

2
Rahim calculated the variance and found it to be -406.4036 kg . Since variance should be
positive, Rahim suspected that he forgot to square one of the data while calculating the sum
of squares of the masses.
Given that other calculation in obtaining the variance were correct, find whose mass was not
squared by Rahim. Show your working clearly.

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 PULAU PINANG PAPER 2 2019

4. Table 4 shows a frequency distributions of the outcome of a power consumption study of 100
houses in a residential park.

Power
Consumption 80-89 90-99 100-109 110-119 120-129 130-139 140-149
(kWh)
Number of
7 14 17 19 21 13 9
houses

Table 4

(a) Find the interquartile range.

(b) During the festive season, the power consumption per household increased by 2
times the original use. Does the interquartile range will change?
Give your reasons.

 SELANGOR SET 1 PAPER 1 2019

22 Given a set of data consists of 5 numbers of a, b, c, d and e. Given the median is 8 and the
variance is 4. Another set data consists 3a + 2, 3b + 2, 3c + 2, 3d + 2 and 3e + 2. Calculate
the value of median and variance.

23 Given that the mean of a set of numbers for  + 2, 2 + 6,  + 1, 2 + 7 and  + 3 is 5.2.

Find the value of . Hence, determine the value of standard deviation.

 SELANGOR SET 1 PAPER 2 2019

5 Table 5 shows times recorded, t minutes, for a group of 200 students to complete a
Mathematics Quiz.

Time (minute), t 16 - 20 21 - 25 26 - 30 31 - 35 36 - 40 41 - 45

Number of students 62 88 16 13 11 10

Table 5

a) Find the mean and the standard deviation of these data.

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b) Due to the technical error, all students took 5 minutes less than the times recorded in
Table 5. Explain the effects this would have on each of the value found in 5(a).

 SELANGOR SET 2 PAPER 1 2019

22 An integer set consists 3, r and 8. The variance for this integer set is .

Find the value of r.

23 Table 23 shows the marks for 30 students in a monthly exam that consists 26 questions.

Score 4-9 10 - 15 16 - 21 22 - 27

Frequency 6 q m 6

Table 23

Given that the median for the data is 16.59. Express q in terms of m.
Hence, if q = 7, find the value of first quartile.

 SELANGOR SET 2 PAPER 2 2019

5 Table 5 shows the frequency distribution of the pH values of soil samples taken from two
orchards.

pH value Orchard A Orchard B

4.4 – 4.8 3 2

4.9 – 5.3 5 7

5.4 – 5.8 5 5

5.9 – 6.3 10 12

6.4 – 6.8 12 8

6.9 – 7.3 5 6

Table 5

Find the mean and standard deviation of the distribution in each orchards. Based on the
values obtained, compared the better soil orchard.

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 TERENGGANU PAPER 1 2019

13 Measures of central tendency is a statistical measurement which is commonly used in daily

life. State the measures of central tendency suitable for the following situations:

a) The heights of the students in 5 Biruni.

b) The income of the parents who have a huge gap in a school in urban areas.
c) Mirza wants to sell favoured food for her school’s Young Entrepreneurship Project.

 TERENGGANU PAPER 2 2019

6 The first set of data x, …, 14, is arranged in ascending order, so does the second data 16, …,
y. Each set of data has 6 values. When the sets of data are combined, x, …, 14, 16, …, y,
the new median is m and the new standard deviation is q.

a) State the value of m.

b) If x and y are removed, state

(i) the new value of m,
(ii) the changes of the value of q.

c) If 3 is multiply and 2 is added to the whole data, find

(i) the new median,
(ii) the new range.

 KEDAH MODUL 1 PAPER 1 2018

18 The set of data 2, 2p, 10, p + 10, 18, 3p + 14 that are arranged in ascending order has mean
k. Given that the interquartile range is 12.
a) Express p in terms of k.
b) Find the value of p.

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 KEDAH MODUL 1 PAPER 2 2018

2 Table 2 shows the frequency distribution of the marks obtained by N students in a test.

Marks Number of students

0–9 4

10 – 19 9

20 – 29 5

30 – 39 p

40 - 49 2

Table 2

a) Given that the median mark is 23.5, find the value of p and of N.
b) Using a scale of 2 cm for 10 marks on the horizontal axis and 2 cm for 1 student on
the vertical axis, draw a histogram to represent the frequency distribution. Find the
mode of the distribution.

 KELANTAN PAPER 1 2018

14 Table 1 shows the frequency distribution of the marks for Additional Mathematics in an exam
for a group of students.

Marks Number of students

1 – 20 3

21 – 40 8

41 – 60 9

61 – 80 8

81 – 100 m

Table 1

Given the minimum mark for 75% of the total students is 70.5 marks and m < 9. Find
a) mode of the marks,
b) value of m.

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 KELANTAN PAPER 2 2018

2 Diagram 1 shows a histogram which represents the distribution of marks for Mathematics
obtained by students of Bestari Class in an examination.

Diagram 1

a) Calculate
(i) the mean mark,
(ii) standard deviation for marks of the students in the class.
b) If the mark of each student is increased by 2, state the variance of the new marks
obtained by the students in the class.

 NEGERI SEMBILAN PAPER 1 2018

20 The mean of 1, 3, 3p, 2p + 6, 4p + 2 and 15 is k.

a) Express p in terms of k.

b) Given the standard deviation of the numbers is √ , find the new variance of the

numbers, in terms of p, if every numbers is added by 2 and then multiplied by 3.

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23 Table 1 shows the frequency distribution of the scores of a group of students in a test.

Score 1 - 10 11 - 20 21 - 30 31 - 40
Frequency 4 14 k 12

Table 1

a) Find the range of the score.

b) Given the median score is 23.625. Find the value of k.

 NEGERI SEMBILAN PAPER 2 2018

1 Use a graph paper to answer this question.

Table 1 shows the scores obtained by 40 pupils in a Mathematical quiz.

Scores ≤5 ≤ 10 ≤ 15 ≤ 20 ≤ 25 ≤ 30 ≤ 35

Number of pupils 0 3 8 17 28 36 40

Table 1

a) Using a scale of 2 cm to 5 scores on the horizontal axis and 2 cm to 1 pupil on the

vertical axis, draw a histogram to represent the frequency distribution of the scores.
Hence, estimate the mode score.
b) State the number of students who obtained more than 25 marks.

 JUJ PAHANG SET 2 PAPER 1 2018

21 Table 21 shows the monthly income earned by an employee of a printing company MZ

Enterprise.
Position Number of employee Income (RM) per head

Supervisor 1 3500

Marketing Executive 1 2500

Graphic Designer 2 2800

Accountant 1 3000

Clerk 3 x

Table 21

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a) Find the value of x, if the mean of the employee’s income is RM 2275.

b) Hence, the company would like to give a bonus to all employees of RM 350.
Calculate the new mode for the employee’s income.

 JUJ PAHANG SET 2 PAPER 1 2018

5 Diagram 5 shows a histogram for the distribution of masses for 30 pupils.

Diagram 5

a) Copy and complete the cumulative frequency table below.

Mass (kg) Frequency Midpoint

20 – 29

30 – 39

40 – 49

50 – 59

60 – 69

b) Find
(i) mean
(ii) variance and standard deviation

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 PERLIS PAPER 1 2018

24 Given 4 and 7 respectively are mode and min for a set of data 3, 4, 4, 6, 10, 12, 12, m, n, with
m > n. Find
a) the value of p and of q
b) median

25 The quartile range and the standard deviation of a set of data are 6 and 2.4 respectively.
If each value in the data is divided by 3 then added by 8, find
a) the new quartile range
b) the new variance.

 PERLIS PAPER 2 2018

4 A teacher wants to select either Ahmad or Luqman to represent the school in a 100 metre
swimming event. Table 1 shows the time taken for each student to complete the swimming
events in six trials.

Time taken to complete a 100 metre swimming event (seconds)

Ahmad 51.3 48.2 52.0 47.3 45.0 52.4

Luqman 52.4 45.9 49.4 51.0 46.5 51.4

Table 1

2
a) Calculate the standard deviation in second , for the time taken by Ahmad and
Luqman to complete the 100 metre swimming event.
b) The teacher will select the student with the best and more consistent performance.
Based on the answer in 4(a), state which student will represent the school in the 100
metre swimming event and give a brief reason.

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 SELANGOR SET A PAPER 1 2018

20 A set of six numbers has a mean of 18 and a standard deviation of √ . When 25 is added to
this set, the mean increases by 1. Find the new variance.

23 The mean and median of 50 pieces of cables are 2.56 m and 2.39 m respectively. After
checking, it is found that a cable of length 4.16 m is wrongly recorded as 3.61 m. Based on
the above information, find the actual mean and median.

 SELANGOR SET A PAPER 2 2018

3 Hafiz and Syafiqah are two best students in 5 Alpha in the Mid Year Examination. Hafiz
obtained an average marks of 66.8 and a standard deviation of 11.36 for the five subjects
while Diagram 3 shows Syafiqah’s results for each of the subject.

Diagram 3

a) Determine whose result is more consistent and justify your answer.

b) An award will be given to either of them after including their marks for English. The
average mark for Hafiz becomes 67.5. Find the minimum marks that Syafiqah should
obtain so that she qualifies for the award.

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 SELANGOR SET B PAPER 1 2018

3 A set of six numbers has a mean of 30. When two numbers a and (a – 6) are added to the
set, the mean becomes 27. Find the value of a.

25 Table 25 shows the number of books borrowed by a group of students in a certain week.

Number of books Frequency

1 3
2 7
3 10
4 x
5 6

Table 25

a) Find the maximum value of x if the mode of number of books borrowed is 3.

b) Find the minimum value of x if the mean of number of books borrowed is more than 3.

 TERENGGANU MPP3 PAPER 1 2018

2
20 A set of data consists of 9, 6, 5, x – 2 and 8. Given the mean is 7, find
a) the positive value of x,
b) the variance using the value of x in (a).

21. Table 21 shows the distribution of the scores obtained by 40 students in a quiz competition.

Marks 0 5 10 15 20

Number of students 2 9 15 11 3

Table 21

Determine the interquartile range of the distribution.

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 TERENGGANU MPP3 PAPER 2 2018

3 Table 3 shows the score obtained by a group of students in a quiz competition.

Scores 10 - 19 20 - 29 30 - 39 40 - 49 50 - 59

Number of students 5 8 k 11 4

Table 3

a) It is given that the first quartile of the scores is 25.75, find the value of k.
b) Find the mean of the scores.
c) Hence, find the standard deviation.

 YIK PAPER 1 2018

14 The sum and the sum of squares of Miss Chua’s monthly income for the first six months in the
year 2015 are RM 12 240 and RM 24 975 000 respectively. Find the standard deviation of
this monthly income within those six months.

 YIK PAPER 2 2018

a) As the Singapore’s coach of 100 m, Mr R will held a series of intensive training and
obtain data for two of the best athletes who are expected to represent the country.
Table 2 shows the time recorded by two athletes, A and B, in the 100 m event during
th
the qualifying session. New rules of 30 SEA Games, specify only one athlete will
represent the country.
Athlete Time (second)
A 10.38 10.40 10.60 10.70 10.82
B 10.48 10.50 10.60 10.62 10.72

Table 2

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th
By using data in Table 2, which athlete qualifies to compete in the 29 SEA Games?

th
b) Table 3 shows time entry for gold medal winner of men final 100 m in the 29 SEA
Games.

Placing Medal Athlete’s Name Country Time (s)

1 Gold Khairul Hafiz Jantan Malaysia 10.38

Table 3

Athlete who was selected by Mr R has trained intensively and can reduce the timing
of 0.35 s constantly for all entries which appear in Table 2. Does the new time entry
allowed him to win the gold medal if Khairul Hafiz Jantan maintain the time record in
th th
30 SEA Games as 29 SEA Games, as shown in Table 3.

 NEGERI SEMBILAN PAPER 1 2017

1 A set of fifteen numbers x1, x2, x3, …, x15 has a standard deviation of √ .
Find
a) the value of ∑( ̅) ,

b) the new variance for , , , …, .

 NEGERI SEMBILAN PAPER 2 2017

1 Table 1 shows the frequency distribution of the mass of a group of students in a class.

Mass (kg) Number of students

40 – 49 6

50 – 59 h

60 – 69 18

70 – 79 16

80 – 89 6

Table 1

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a) It is given that the third quartile mass of the distribution is 74.5 kg. Calculate the
value of h.
b) Using a scale of 2 cm to 10 kg on the horizontal axis and 2 cm to 2 students on the
vertical axis, draw a histogram to represent the frequency distribution of the mass.
Hence, estimate the mode of the mass.
c) What is the mode mass if the mass of each student is increased by 4 kg?

 PAHANG PAPER 1 2017

25 A set of data consists of 2, 3, 6 and 9.

a) Determine the mean and the standard deviation of the data.
b) Two numbers,  and , are to be added to this set of data, such that the mean is
increased by 1 and the variance is increased by 2.5. Find the value of  and the
value of .

 PAHANG PAPER 2 2017

2 Encik Syukri pays RM x income tax every month for his tax assessment in the year 2015.
Table 2 shows the sum and the sum of squares of x.

∑ 30 000

∑ 75 019 200

Table 2

a) Find the standard deviation of his income tax.

b) Starting from the year 2016, Encik Syukri needs to pay an additional of RM 2500
every month because of the improvement performance of his business. Find the
mean and the standard deviation of his income tax for his tax assessment in the year
2016.

 PERLIS PAPER 1 2017

24 The mean of 8 numbers of 2, 3, p, 6, 3p – 2, 10, 13 and 16 is 8.

a) Find the value of p.
b) If each number is multiplied by 2 and then 4 is added to it, find the mean.

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25 Table 25 shows the frequency distribution for the marks obtained by a group of students.

Score Frequency

15 – 19 1

20 – 24 8

25 – 29 6

30 – 34 5

35 - 39 4

Table 25

Calculate the standard deviation of the marks.

 TERENGGANU BK7 PAPER 1 2016

9 A set of 15 numbers has a variance of 54 and it is given that ∑ . Find

a) the mean, ̅
b) the value of ∑ .

10 The mean of a set of data 1, x, 2x, 9, 10 and 16 is y. If each value in the set is decreased by

6, the new mean is y. Find the values of x and of y.

 TERENGGANU BK7 PAPER 2 2016

5 Table 5 shows the information of the group P and group Q.

Group Number of group members Total age (year) Standard deviation

P 4 k 36

Q 5 150 m

Table 5

a) Given the mean age of the members of group P is 48, find the value of k.
b) (i) For group Q, ∑( ̅) , find the value of m.
(ii) Hence, find the sum of squares of the age group Q members.
c) Calculate the mean and the variance of the combined groups age.

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