A free Sec 2 Maths worksheet on statistics: 7 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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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
1
Number of books borrowed
1
2
3
4
5
6
Frequency
7
8
3
3
9
8
The frequency table shows the number of library books borrowed by each pupil in a week. Find the median.
Answer[2]
2
The histogram shows the heights, h cm, of some seedlings after two weeks. Find the number of seedlings with 8<h≤16.
Answer[2]
3
(a)A class of 40 pupils each chooses a favourite CCA. The teacher wants to show what fraction of the class chose each CCA. Which statistical diagram is the most suitable?
Answer (a)[1]
(b)The numbers of goals scored by a team in each of its 16 matches (from 0 to 6) are to be shown so that the most common score stands out. Which statistical diagram is the most suitable?
Answer (b)[1]
4
Marks (x)
Frequency
24<x≤28
6
28<x≤32
5
32<x≤36
10
36<x≤40
7
40<x≤44
8
44<x≤48
9
The table shows the marks of some pupils in a test. Using the mid-value of each class, calculate an estimate of the mean, correct to 3 significant figures.
Answermarks[3]
Section B
5
(a)The diagram is an example of a dot diagram. Which statement about dot diagrams is true?
Answer (a)[1]
Number of siblings
0
1
2
3
4
5
Frequency
8
2
2
4
1
k
(b)The frequency table shows the number of siblings of each pupil in a class. The median is 5. Find the smallest possible value of k.
Answer (b)[2]
(c)The histogram shows the masses, m kg, of the pupils in a Secondary 2 class. Find the percentage of the pupils with m≤50.
Answer (c)%[3]
6
(a)The histogram shows the heights, h cm, of some seedlings after two weeks. Find the number of seedlings with 12<h≤20.
Answer (a)[2]
Number of people in the household
1
2
3
4
5
Frequency
8
3
5
2
7
(b)The frequency table shows the number of people in each household in an HDB block. Find the median.
Answer (b)[2]
(c)The mean score of 6 pupils in a test is 4.5 marks. The score of one more pupil, 6.6 marks, is included. Find the new mean score.
Answer (c)[3]
7
(a)(i)The ages of 30 people at a community event (from 18 to 75) are to be shown so that each age is kept and the shape of the data can be seen. Which statistical diagram is the most suitable?
Answer (a)(i)[1]
(a)(ii)The numbers of brothers and sisters of each of the 20 pupils in a class (from 0 to 5) are to be shown so that every pupil's value can be seen. Which statistical diagram is the most suitable?
Answer (a)(ii)[1]
(b)(i)The numbers of minutes 8 pupils took to travel to school are 22,22,20,21,23,44,25,22. Find the median.
Answer (b)(i)[2]
(b)(ii)The marks scored by 9 pupils in a quiz are 8,10,3,6,6,6,4,8,6. Find the mode.
Answer (b)(ii)[1]
(c)The dot diagram shows the number of siblings of each pupil in a class. Find the mean, correct to 3 significant figures.
Answer (c)[3]
END OF PAPER
Answers and worked solutions
Question 1
Answer: Median =4[2]
Total frequency =7+8+3+3+9+8=38Running totals: 7,15,18,21,30,38The median is the mean of the 19th and 20th values.Median =4
Question 2
Answer: 21 of the seedlings have 8<h≤16.[2]
8<h≤16: the classes 8<h≤12 to 12<h≤16.6+15=2121 of the seedlings have 8<h≤16.
Question 3
(a)Answer: PIE[1]
The diagram has to show each part as a share of a whole.Pie chart.
(b)Answer: DOT[1]
The diagram has to show a small set of data with only a few different values.Dot diagram.
Question 4
Answer: =36.9 marks (3 s.f.)[3]
Mid-values: 26,30,34,38,42,46Total frequency =6+5+10+7+8+9=45Total =26×6+30×5+34×10+38×7+42×8+46×9=1662Mean =451662=36.9333…=36.9 marks (3 s.f.)
Question 5
(a)Answer: D[1]
It cannot show the mode. False.The dots must be joined with straight lines. False.It is a good choice for a very large set of data such as 1000 values. False.It shows how spread out the data are. True.D: It shows how spread out the data are.