Sec 2 G2 Maths Data handling and analysis worksheet with answers
A free Sec 2 G2 Maths worksheet on data handling and analysis: 8 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 diagram is an example of a histogram. Which statement about histograms is true?
Answer[1]
2
The stem-and-leaf diagram shows the number of passengers on each bus trip. Find the median.
Answerpassengers[2]
3
Height (h cm)
Frequency
10<h≤20
13
20<h≤30
6
30<h≤40
11
40<h≤50
2
50<h≤60
15
60<h≤70
5
The table shows the heights of some plants. Using the mid-value of each class, calculate an estimate of the mean, correct to 3 significant figures.
Answercm[3]
4
(a)The heights, in cm, of 9 seedlings are 11,16,25,9,16,28,24,21,10. Find the median.
Answer (a)[2]
(b)The mean time of 4 runners for a 2.4 km run is 3.6 min. When the time of one more runner is included, the mean time of the 5 runners becomes 3.36 min. Find the time of this runner.
Answer (b)[3]
Section B
5
Number of CCAs
0
1
2
3
4
5
Frequency
3
6
5
8
6
9
(a)The frequency table shows the number of co-curricular activities each pupil takes part in. Find the median.
Answer (a)[2]
Time (t minutes)
Frequency
0<t≤5
5
5<t≤10
9
10<t≤15
9
15<t≤20
15
20<t≤25
2
(b)The table shows the time taken by some pupils to finish a puzzle. Find the class that contains the median.
Answer (b)[2]
6
(a)The histogram shows the masses, m kg, of the pupils in a Secondary 2 class. Complete the frequency table.
Answer (a)[2]
Score
6
7
8
9
10
11
Frequency
3
1
1
6
1
k
(b)The frequency table shows the scores of pupils in a 10-mark spelling test. The median is 11. Find the smallest possible value of k.
Answer (b)[2]
7
(a)The diagram is an example of a histogram. Which statement about histograms is true?
Answer (a)[1]
Number of CCAs
0
1
2
3
4
Frequency
7
6
1
8
6
(b)The frequency table shows the number of co-curricular activities each pupil takes part in. Find the mode.
Answer (b)[1]
Mass (m kg)
Frequency
10<m≤20
11
20<m≤30
4
30<m≤40
3
40<m≤50
12
(c)The table shows the masses of some parcels at a post office. Using the mid-value of each class, calculate an estimate of the mean, correct to 3 significant figures.
Answer (c)kg[3]
8
(a)The diagram is an example of a histogram. Which statement about histograms is true?
Answer (a)[1]
(b)The histogram shows the masses, m kg, of the pupils in a Secondary 2 class. Find the number of pupils with m≤50.
Answer (b)[2]
Mass (m kg)
Frequency
10<m≤20
13
20<m≤30
3
30<m≤40
10
40<m≤50
13
50<m≤60
14
(c)The table shows the masses of some parcels at a post office. Using the mid-value of each class, calculate an estimate of the mean, correct to 3 significant figures.
Answer (c)kg[3]
END OF PAPER
Answers and worked solutions
Question 1
Answer: C[1]
Each data value can be read exactly from it. False.The classes may overlap. False.It is used for grouped continuous data such as heights or times. True.There should be gaps between the bars as in a bar graph. False.C: It is used for grouped continuous data such as heights or times.
Question 2
Answer: =49 passengers[2]
Number of values =12The median is the mean of the 6th and 7th values.Median =249+49=49 passengers
Question 3
Answer: =37.9 cm (3 s.f.)[3]
Mid-values: 15,25,35,45,55,65Total frequency =13+6+11+2+15+5=52Total =15×13+25×6+35×11+45×2+55×15+65×5=1970Mean =521970=37.8846…=37.9 cm (3 s.f.)
Question 4
(a)Answer: Median =16 cm[2]
9,10,11,16,16,21,24,25,28The middle value is the 29+1=5th value.Median =16 cm
(b)Answer: =2.4 min[3]
Total =3.6×4=14.4New total =3.36×5=16.8Added value =16.8−14.4=2.4 min
Question 5
(a)Answer: Median =3[2]
Total frequency =3+6+5+8+6+9=37Running totals: 3,9,14,22,28,37The median is the 237+1=19th value.Median =3
(b)Answer: 10 < t ≤ 15[2]
Total frequency =5+9+9+15+2=40The median is the mean of the 20th and 21th values.Running totals: 5,14,23,38,40The running total first reaches 20 in the class 10<t≤15, so the median lies in it.
Question 6
(a)Answer: 50<m≤55: the bar's height is 10.[2]
40<m≤45: the bar's height is 1.45<m≤50: the bar's height is 3.50<m≤55: the bar's height is 10.
Each data value can be read exactly from it. False.It is the best diagram for categories such as favourite colours. False.The bars touch because the classes follow on from one another. True.There should be gaps between the bars as in a bar graph. False.C: The bars touch because the classes follow on from one another.
(b)Answer: Mode =3[1]
The highest frequency is 8.Mode =3
(c)Answer: =30.3 kg (3 s.f.)[3]
Mid-values: 15,25,35,45Total frequency =11+4+3+12=30Total =15×11+25×4+35×3+45×12=910Mean =30910=30.3333…=30.3 kg (3 s.f.)
Question 8
(a)Answer: B[1]
There should be gaps between the bars as in a bar graph. False.The original data values cannot be read from it. True.It is the best diagram for categories such as favourite colours. False.Each data value can be read exactly from it. False.B: The original data values cannot be read from it.
(b)Answer: 16 of the pupils have m≤50.[2]
m≤50: the classes 40<m≤45 to 45<m≤50.6+10=1616 of the pupils have m≤50.
(c)Answer: =37.3 kg (3 s.f.)[3]
Mid-values: 15,25,35,45,55Total frequency =13+3+10+13+14=53Total =15×13+25×3+35×10+45×13+55×14=1975Mean =531975=37.2641…=37.3 kg (3 s.f.)