Sec 3 G1 Maths Statistics worksheet with answers

A free Sec 3 G1 Maths worksheet on statistics: 9 questions, 30 marks, short questions first and then structured ones, in the school exam style. The answers and full worked solutions are on the last page.

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Sec 3 G1 Maths worksheet: Statistics

Total: 30 marksSuggested time: 50 minutes

Name: ______________________________Class: ____________ Date: ____________

Answer all questions. Show all your working. Give non-exact answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless the question says otherwise.

Section A

Marks, $x$	Frequency
$0 < x \le 10$	3
$10 < x \le 20$	10
$20 < x \le 30$	15
$30 < x \le 40$	20
$40 < x \le 50$	8
$50 < x \le 60$	4

The table shows the marks of

60

students in a test. Find the number of students who scored

20

marks or fewer.

Answer[1]

The cumulative frequency curve shows the marks of

70

students in a test. Use the curve to estimate the number of students who scored at most

35

marks.

Answer[1]

Find the median of

48, \ 52, \ 39, \ 61, \ 44, \ 57, \ 50, \ 46, \ 55, \ 42

Answer[2]

Find the median of

9, \ 3, \ 12, \ 7, \ 15, \ 10, \ 8, \ 6

Answer[2]

(a)The frequency table shows the time, in minutes, that

60

students took to finish a puzzle. Complete the cumulative frequency column.

Answer (a)[2]

(b)The cumulative frequency table shows the marks of

50

students in a test. Complete the frequency column.

Answer (b)[2]

(a)Find the median of

14, \ 11, \ 20, \ 16, \ 9, \ 13, \ 18

Answer (a)[2]

(b)Find the interquartile range of

17, \ 23, \ 19, \ 31, \ 26, \ 14, \ 28, \ 22, \ 20, \ 25, \ 18

Answer (b)[3]

Section B

(a)The cumulative frequency curve shows the marks of

50

students. Use the curve to estimate the upper quartile.

Answer (a)[1]

(b)(i)The frequency table shows the marks of

60

students in a test. Complete the cumulative frequency column.

Answer (b)(i)[2]

(b)(ii)The cumulative frequency table shows the time, in minutes, that

60

students took to finish a puzzle. Complete the frequency column.

Answer (b)(ii)[2]

(a)The cumulative frequency table shows the time, in minutes, that

50

students took to finish a puzzle. Complete the frequency column.

Answer (a)[2]

(b)Find the interquartile range of

91, \ 84, \ 77, \ 88, \ 95, \ 80, \ 86, \ 73, \ 90, \ 82

Answer (b)[3]

(a)The cumulative frequency curve shows the marks of

60

students. Use the curve to estimate the median mark.

Answer (a)[1]

(b)Find the median of

8, \ 6, \ 11, \ 4, \ 9, \ 7, \ 12, \ 5, \ 10, \ 2, \ 14

Answer (b)[2]

(c)The cumulative frequency curve shows the marks of

50

students in a test. Use the curve to estimate the number of students who scored more than

35

marks.

Answer (c)[2]

END OF PAPER

Answers and worked solutions

Question 1

Answer:

\text{Cumulative frequency} = 13

[1]

\mathstrut 3 + 10

\text{Cumulative frequency} = 13

Question 2

Answer: The curve gives about

40

students with at most

35

marks.[1]

The curve gives about

40

students with at most

35

marks.

Question 3

Answer:

\text{Median} = 49

[2]

39, \ 42, \ 44, \ 46, \ 48, \ 50, \ 52, \ 55, \ 57, \ 61

n = 10

Position: the 5.5th value, halfway between the 5th and 6th values.

\mathstrut \text{Median} = \dfrac{48 + 50}{2}

\text{Median} = 49

Question 4

Answer:

\text{Median} = 8.5

[2]

3, \ 6, \ 7, \ 8, \ 9, \ 10, \ 12, \ 15

n = 8

Position: the 4.5th value, halfway between the 4th and 5th values.

\mathstrut \text{Median} = \dfrac{8 + 9}{2}

\text{Median} = 8.5

Question 5

(a)Answer: Cumulative frequencies:

3, \ 10, \ 22, \ 40, \ 54, \ 60

[2]

\text{1st} = 3

\mathstrut \text{2nd} = 3 + 7

\text{2nd} = 10

\text{Last} = 60

Cumulative frequencies:

3, \ 10, \ 22, \ 40, \ 54, \ 60

(b)Answer: Frequencies:

1, \ 6, \ 10, \ 15, \ 12, \ 6

[2]

\text{1st} = 1

\mathstrut \text{2nd} = 7 - 1

\text{2nd} = 6

\text{Total} = 50

Frequencies:

1, \ 6, \ 10, \ 15, \ 12, \ 6

Question 6

(a)Answer:

\text{Median} = 14

[2]

9, \ 11, \ 13, \ 14, \ 16, \ 18, \ 20

n = 7

The middle value is the 4th.

\text{Median} = 14

(b)Answer:

\text{IQR} = 8

[3]

14, \ 17, \ 18, \ 19, \ 20, \ 22, \ 23, \ 25, \ 26, \ 28, \ 31

n = 11

\text{Lower half: } 14, \ 17, \ 18, \ 19, \ 20

\text{Upper half: } 23, \ 25, \ 26, \ 28, \ 31

Q_1 = 18

Q_3 = 26

\mathstrut \text{IQR} = 26 - 18

\text{IQR} = 8

Question 7

(a)Answer:

Q_3 \approx 37.1

[1]

\mathstrut \dfrac{3 \times 50}{4} = 37.5

Q_3 \approx 37.1

(b)(i)Answer: Cumulative frequencies:

3, \ 13, \ 28, \ 48, \ 56, \ 60

[2]

\text{1st} = 3

\mathstrut \text{2nd} = 3 + 10

\text{2nd} = 13

\text{Last} = 60

Cumulative frequencies:

3, \ 13, \ 28, \ 48, \ 56, \ 60

(b)(ii)Answer: Frequencies:

2, \ 6, \ 14, \ 22, \ 11, \ 5

[2]

\text{1st} = 2

\mathstrut \text{2nd} = 8 - 2

\text{2nd} = 6

\text{Total} = 60

Frequencies:

2, \ 6, \ 14, \ 22, \ 11, \ 5

Question 8

(a)Answer: Frequencies:

5, \ 11, \ 14, \ 10, \ 6, \ 4

[2]

\text{1st} = 5

\mathstrut \text{2nd} = 16 - 5

\text{2nd} = 11

\text{Total} = 50

Frequencies:

5, \ 11, \ 14, \ 10, \ 6, \ 4

(b)Answer:

\text{IQR} = 10

[3]

73, \ 77, \ 80, \ 82, \ 84, \ 86, \ 88, \ 90, \ 91, \ 95

n = 10

\text{Lower half: } 73, \ 77, \ 80, \ 82, \ 84

\text{Upper half: } 86, \ 88, \ 90, \ 91, \ 95

Q_1 = 80

Q_3 = 90

\mathstrut \text{IQR} = 90 - 80

\text{IQR} = 10

Question 9

(a)Answer:

\text{Median} \approx 33.7

[1]

\mathstrut \dfrac{60}{2} = 30

\text{Median} \approx 33.7

(b)Answer:

\text{Median} = 8

[2]

2, \ 4, \ 5, \ 6, \ 7, \ 8, \ 9, \ 10, \ 11, \ 12, \ 14

n = 11

The middle value is the 6th.

\text{Median} = 8

(c)Answer:

\text{Number} \approx 19

[2]

The curve gives about

31

students with at most

35

marks.

\mathstrut 50 - 31

\text{Number} \approx 19

Sec 3 G1 Maths Statistics worksheet with answers

In the print window, choose Save as PDF to download it.

Or practise it online with step-by-step help when you get one wrong.

Section A

Marks, $x$	Frequency
$0 < x \le 10$	3
$10 < x \le 20$	10
$20 < x \le 30$	15
$30 < x \le 40$	20
$40 < x \le 50$	8
$50 < x \le 60$	4

The table shows the marks of

60

students in a test. Find the number of students who scored

20

marks or fewer.

Answer[1]

Section B

(a)The cumulative frequency curve shows the marks of

50

students. Use the curve to estimate the upper quartile.

Answer (a)[1]

(b)(i)The frequency table shows the marks of

60

students in a test. Complete the cumulative frequency column.

Answer (b)(i)[2]

(b)(ii)The cumulative frequency table shows the time, in minutes, that

60

students took to finish a puzzle. Complete the frequency column.

Answer (b)(ii)[2]

Answers and worked solutions

Question 1

Answer:

\text{Cumulative frequency} = 13

[1]

\mathstrut 3 + 10

\text{Cumulative frequency} = 13

Question 2

Answer: The curve gives about

40

students with at most

35

marks.[1]

The curve gives about

40

students with at most

35

marks.

Question 3

Answer:

\text{Median} = 49

[2]

39, \ 42, \ 44, \ 46, \ 48, \ 50, \ 52, \ 55, \ 57, \ 61

n = 10

Position: the 5.5th value, halfway between the 5th and 6th values.

\mathstrut \text{Median} = \dfrac{48 + 50}{2}

\text{Median} = 49

Question 4

Answer:

\text{Median} = 8.5

[2]

3, \ 6, \ 7, \ 8, \ 9, \ 10, \ 12, \ 15

n = 8

Position: the 4.5th value, halfway between the 4th and 5th values.

\mathstrut \text{Median} = \dfrac{8 + 9}{2}

\text{Median} = 8.5

Question 5

(a)Answer: Cumulative frequencies:

3, \ 10, \ 22, \ 40, \ 54, \ 60

[2]

\text{1st} = 3

\mathstrut \text{2nd} = 3 + 7

\text{2nd} = 10

\text{Last} = 60

Cumulative frequencies:

3, \ 10, \ 22, \ 40, \ 54, \ 60

(b)Answer: Frequencies:

1, \ 6, \ 10, \ 15, \ 12, \ 6

[2]

\text{1st} = 1

\mathstrut \text{2nd} = 7 - 1

\text{2nd} = 6

\text{Total} = 50

Frequencies:

1, \ 6, \ 10, \ 15, \ 12, \ 6

Question 6

(a)Answer:

\text{Median} = 14

[2]

9, \ 11, \ 13, \ 14, \ 16, \ 18, \ 20

n = 7

The middle value is the 4th.

\text{Median} = 14

(b)Answer:

\text{IQR} = 8

[3]

14, \ 17, \ 18, \ 19, \ 20, \ 22, \ 23, \ 25, \ 26, \ 28, \ 31

n = 11

\text{Lower half: } 14, \ 17, \ 18, \ 19, \ 20

\text{Upper half: } 23, \ 25, \ 26, \ 28, \ 31

Q_1 = 18

Q_3 = 26

\mathstrut \text{IQR} = 26 - 18

\text{IQR} = 8

Question 7

(a)Answer:

Q_3 \approx 37.1

[1]

\mathstrut \dfrac{3 \times 50}{4} = 37.5

Q_3 \approx 37.1

(b)(i)Answer: Cumulative frequencies:

3, \ 13, \ 28, \ 48, \ 56, \ 60

[2]

\text{1st} = 3

\mathstrut \text{2nd} = 3 + 10

\text{2nd} = 13

\text{Last} = 60

Cumulative frequencies:

3, \ 13, \ 28, \ 48, \ 56, \ 60

(b)(ii)Answer: Frequencies:

2, \ 6, \ 14, \ 22, \ 11, \ 5

[2]

\text{1st} = 2

\mathstrut \text{2nd} = 8 - 2

\text{2nd} = 6

\text{Total} = 60

Frequencies:

2, \ 6, \ 14, \ 22, \ 11, \ 5

Question 8

(a)Answer: Frequencies:

5, \ 11, \ 14, \ 10, \ 6, \ 4

[2]

\text{1st} = 5

\mathstrut \text{2nd} = 16 - 5

\text{2nd} = 11

\text{Total} = 50

Frequencies:

5, \ 11, \ 14, \ 10, \ 6, \ 4

(b)Answer:

\text{IQR} = 10

[3]

73, \ 77, \ 80, \ 82, \ 84, \ 86, \ 88, \ 90, \ 91, \ 95

n = 10

\text{Lower half: } 73, \ 77, \ 80, \ 82, \ 84

\text{Upper half: } 86, \ 88, \ 90, \ 91, \ 95

Q_1 = 80

Q_3 = 90

\mathstrut \text{IQR} = 90 - 80

\text{IQR} = 10

Question 9

(a)Answer:

\text{Median} \approx 33.7

[1]

\mathstrut \dfrac{60}{2} = 30

\text{Median} \approx 33.7

(b)Answer:

\text{Median} = 8

[2]

2, \ 4, \ 5, \ 6, \ 7, \ 8, \ 9, \ 10, \ 11, \ 12, \ 14

n = 11

The middle value is the 6th.

\text{Median} = 8

(c)Answer:

\text{Number} \approx 19

[2]

The curve gives about

31

students with at most

35

marks.

\mathstrut 50 - 31

\text{Number} \approx 19