A free Sec 2 G1 Maths worksheet on statistics: 10 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
The histogram shows the times, s seconds, of the runners in a 100 m race. Write down the number of runners in the class 15<s≤16.
Answer[1]
2
The dot diagram shows the shoe sizes of the members of a running club. Find the median.
Answer[2]
3
(a)The masses of 120 durians are grouped in equal classes of 0.5 kg and the frequencies are to be shown. Which statistical diagram is the most suitable?
Answer (a)[1]
(b)The lengths of 220 leaves are grouped in equal classes of 2 cm and the frequencies are to be shown. Which statistical diagram is the most suitable?
Answer (b)[1]
4
The stem-and-leaf diagram shows the times taken by runners to complete a 5 km race. Find the range.
Answerminutes[2]
5
The histogram shows the time, t minutes, that some pupils spent on homework last night. Find the total number of pupils.
Answer[2]
6
The numbers of minutes 5 pupils took to travel to school are 24,43,x,15,11. The mean is 20 min. Find x.
Answer[3]
7
The heights, in cm, of 6 seedlings are 14,12,11,27,x,30. The mean is 19 cm. Find x.
Answer[3]
Section B
8
(a)The histogram shows the marks, x, of some pupils in a test. Write down the modal class.
Answer (a)[1]
(b)(i)The scores (from 0 to 10) of each of the 18 pupils in a spelling quiz are to be shown so that every score can be seen. Which statistical diagram is the most suitable?
Answer (b)(i)[1]
(b)(ii)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)(ii)[1]
(c)The dot diagram shows the number of goals a team scored in each match. Find the median.
Answer (c)[2]
9
(a)The diagram is an example of a dot diagram. Which statement about dot diagrams is true?
Answer (a)[1]
(b)The histogram shows the time, t minutes, that some pupils spent on homework last night. Find the number of pupils with t>30.
Answer (b)[2]
(c)The numbers of books read by 5 pupils last month are 8,4,3,1,8. Find the mean.
Answer (c)[2]
10
(a)The dot diagram shows the number of hours some pupils slept last night. Find the mode.
Answer (a)[1]
(b)The histogram shows the masses, m kg, of the pupils in a Secondary 2 class. Complete the frequency table.
Answer (b)[2]
(c)The numbers of books read by 9 pupils last month are 5,9,1,4,0,3,4,9,6. Find the median.
Answer (c)[2]
END OF PAPER
Answers and worked solutions
Question 1
Answer: Frequency =9[1]
The class 15<s≤16 is the bar from 15 to 16.Frequency =9There are 9 runners in this class.
Question 2
Answer: =41[2]
Number of values =16The median is the mean of the 8th and 9th values.Median =241+41=41
Question 3
(a)Answer: HIST[1]
The diagram has to show grouped continuous data in equal classes.Histogram.
(b)Answer: HIST[1]
The diagram has to show grouped continuous data in equal classes.Histogram.
Question 4
Answer: =34 minutes[2]
Largest value =58 minutes, smallest value =24 minutesRange =58−24=34 minutes
Total =20×5=100Sum of the others =24+43+15+11=93x=100−93=7
Question 7
Answer: =20[3]
Total =19×6=114Sum of the others =14+12+11+27+30=94x=114−94=20
Question 8
(a)Answer: 40 < x ≤ 50[1]
The tallest bar has frequency 12.The modal class is 40<x≤50.
(b)(i)Answer: DOT[1]
The diagram has to show a small set of data with only a few different values.Dot diagram.
(b)(ii)Answer: DOT[1]
The diagram has to show a small set of data with only a few different values.Dot diagram.
(c)Answer: =4[2]
Number of values =16The median is the mean of the 8th and 9th values.Median =24+4=4
Question 9
(a)Answer: C[1]
It shows each value as a share of the whole. False.It cannot show the mode. False.Every data value is shown by its own dot. True.It is a good choice for a very large set of data such as 1000 values. False.C: Every data value is shown by its own dot.
(b)Answer: 41 of the pupils have t>30.[2]
t>30: the classes 30<t≤40 to 60<t≤70 (a value of exactly 30 is in the class below).14+9+8+10=4141 of the pupils have t>30.
(c)Answer: =4.8[2]
Sum =8+4+3+1+8=24Mean =524=4.8
Question 10
(a)Answer: Mode =8[1]
The tallest column has 5 dots.Mode =8
(b)Answer: 55<m≤60: the bar's height is 13.[2]
40<m≤45: the bar's height is 14.50<m≤55: the bar's height is 3.55<m≤60: the bar's height is 13.
(c)Answer: Median =4[2]
0,1,3,4,4,5,6,9,9The middle value is the 29+1=5th value.Median =4