The frequency table shows the times, t minutes, taken by 35 students to finish a puzzle.
Time (t minutes)
Frequency
0 < t ≤ 5
8
5 < t ≤ 10
12
10 < t ≤ 15
9
15 < t ≤ 20
6
Noah makes a cumulative frequency table for this data. He writes the cumulative frequencies 8, 20, 29, 34.
Explain what is wrong with Noah's cumulative frequencies.
1 mark
Show answer
The final cumulative frequency should be 35 (the total frequency), not 34 - the last value is wrong (29 + 6 = 35)
2
The table shows the masses, m grams, of 40 tomatoes.
Mass (m grams)
Frequency
50 < m ≤ 60
5
60 < m ≤ 70
11
70 < m ≤ 80
14
80 < m ≤ 90
7
90 < m ≤ 100
3
Complete the cumulative frequency table.
Mass (m grams)
Cumulative frequency
50 < m ≤ 60
50 < m ≤ 70
50 < m ≤ 80
50 < m ≤ 90
50 < m ≤ 100
2 marks
Show answer
up to 60) 5up to 70) 16up to 80) 30up to 90) 37up to 100) 40
3
The table shows the ages, a years, of the 60 members of a running club.
Age (a years)
Frequency
10 < a ≤ 20
9
20 < a ≤ 30
15
30 < a ≤ 40
18
40 < a ≤ 50
12
50 < a ≤ 60
6
Complete a cumulative frequency table for this data.
Write down the class interval that contains the median age.
3 marks
Show answer
a) 9, 24, 42, 54, 60b) 30 < a <= 40
4
40 students took a typing test. Salma drew a cumulative frequency graph for their times.
Salma plotted each cumulative frequency against the midpoint of its class interval.
Explain the mistake Salma made.
Salma redraws the graph correctly. The correct graph shows a cumulative frequency of 34 at a time of 40 seconds. How many students took longer than 40 seconds?
What percentage of the 40 students took longer than 40 seconds?
3 marks
Show answer
a) She should plot each cumulative frequency at the upper end (upper class boundary) of the interval, not the midpointb) 6c) 15%
5
The table shows the heights, h cm, of 80 sunflower seedlings.
Height (h cm)
Frequency
0 < h ≤ 10
6
10 < h ≤ 20
14
20 < h ≤ 30
26
30 < h ≤ 40
22
40 < h ≤ 50
12
Complete the cumulative frequency table.
On the grid, draw a cumulative frequency graph for this information.
Use your graph to find an estimate for the median height.
Use your graph to find an estimate for the interquartile range of the heights.
6 marks
Show answer
a) 6, 20, 46, 68, 80b) points at (10,6),(20,20),(30,46),(40,68),(50,80) joined by a smooth curve through the originc) approximately 28 cm (accept 26-29)d) approximately 16 cm (accept 14-19)
6
The table shows the journey times, t minutes, of 60 commuters.
Time (t minutes)
Frequency
0 < t ≤ 10
4
10 < t ≤ 20
10
20 < t ≤ 30
17
30 < t ≤ 40
15
40 < t ≤ 50
9
50 < t ≤ 60
5
Complete the cumulative frequency table.
On the grid, draw a cumulative frequency graph for this information.
Use your graph to find an estimate for the median journey time.
Use your graph to estimate the percentage of commuters whose journey took more than 45 minutes.
6 marks
Show answer
a) 4, 14, 31, 46, 55, 60b) points at (10,4),(20,14),(30,31),(40,46),(50,55),(60,60) joined by a smooth curvec) approximately 29 minutes (accept 28-31)d) approximately 16% (accept 13-20%)
7
The table shows the lengths, t minutes, of 40 phone calls.
Length (t minutes)
Frequency
0 < t ≤ 5
6
5 < t ≤ 10
14
10 < t ≤ 15
12
15 < t ≤ 20
8
Complete a cumulative frequency table for this data.
How many calls lasted 10 minutes or less?
Estimate the number of calls that lasted more than 12 minutes. Assume the calls in each class are spread evenly.
4 marks
Show answer
a) 6, 20, 32, 40b) 20c) 15
8
The cumulative frequency table shows the marks of 60 students in a test.
Mark
Cumulative frequency
up to 20
5
up to 40
18
up to 60
41
up to 80
57
up to 100
60
How many students scored more than 40 marks and up to 60 marks?
How many students scored more than 80 marks?
Estimate the median mark. Assume the marks in each class are spread evenly.
4 marks
Show answer
a) 23b) 3c) 50.4
9
The cumulative frequency graph shows the test scores of the 60 students in Class A.
Use the graph to find an estimate for the median score.
Use the graph to find an estimate for the interquartile range of the scores.
The 60 students in Class B had a median score of 45 and an interquartile range of 12. Compare the scores of the two classes.
6 marks
Show answer
a) approximately 32 (accept 31-34)b) approximately 18 (accept 15-21)c) Class B has the higher median (45 vs about 32) so did better on average; Class B has the smaller IQR (12 vs about 18) so its scores are less spread out
10
The cumulative frequency graph shows the weights, in kg, of 80 parcels sent from a depot on Monday.
The lightest parcel weighed 0.5 kg and the heaviest weighed 9.5 kg.
Use the graph to draw a box plot for the weights of Monday's parcels.
Use the graph to estimate the number of parcels that weighed more than 7 kg.
On Tuesday the parcels had a median weight of 4.4 kg and an interquartile range of 2.1 kg. Compare the weights of Monday's and Tuesday's parcels.
6 marks
Show answer
a) min 0.5, LQ approximately 3.75 (accept 3.5-4), median approximately 5.2 (accept 5-5.4), UQ approximately 6.8 (accept 6.5-7.1), max 9.5b) approximately 18 (accept 15-21)c) Monday's median is higher so Monday's parcels were heavier on average; Monday's IQR is larger so Monday's weights varied more
11
The table shows the heights, h cm, of 80 plants.
Height (h cm)
Frequency
0 < h ≤ 20
8
20 < h ≤ 40
22
40 < h ≤ 60
30
60 < h ≤ 80
14
80 < h ≤ 100
6
Complete a cumulative frequency table for this data.
Estimate the median height.
Estimate the interquartile range.
Assume the heights in each class are spread evenly.
6 marks
Show answer
a) 8, 30, 60, 74, 80b) 46.7 cmc) 29.1 cm
12
The table shows the commute times, t minutes, of 100 office workers.
Time (t minutes)
Frequency
0 < t ≤ 15
12
15 < t ≤ 30
30
30 < t ≤ 45
34
45 < t ≤ 60
18
60 < t ≤ 75
6
How many workers have a commute of 30 minutes or less?
Write down the class interval that contains the median commute time.
Write down the class interval that contains the upper quartile.
A local newspaper claims that more than a third of the workers commute for over 45 minutes. Is the claim correct? Show your working.
6 marks
Show answer
a) 42b) 30 < t <= 45c) 30 < t <= 45d) No; 24 out of 100 (24%) commute over 45 minutes, and 24% is less than a third
13
80 students sat an exam marked out of 100. The table shows their scores, s marks.
Score (s marks)
Frequency
0 < s ≤ 20
6
20 < s ≤ 40
18
40 < s ≤ 60
28
60 < s ≤ 80
20
80 < s ≤ 100
8
Complete the cumulative frequency table.
Write down the class interval that contains the median score.
A cumulative frequency graph of the data gives these estimates: median 51, lower quartile 37, upper quartile 66. Work out an estimate for the interquartile range.
The pass mark was 60. Work out the percentage of students who scored more than 60.
Last year the same exam had a median of 46 and an interquartile range of 24. Compare this year's scores with last year's.
7 marks
Show answer
a) 6, 24, 52, 72, 80b) 40 < s <= 60c) 29d) 35%e) Higher median this year (51 vs 46) so better on average; larger IQR this year (29 vs 24) so more spread out
14
The table shows the waiting times, t minutes, of 120 customers in a cafe.
Waiting time (t minutes)
Frequency
0 < t ≤ 2
15
2 < t ≤ 4
35
4 < t ≤ 6
40
6 < t ≤ 8
20
8 < t ≤ 10
10
Complete a cumulative frequency table for this data.
Estimate the 90th percentile of the waiting times. Assume the times in each class are spread evenly.
The cafe says that "at least 90% of customers wait 8 minutes or less". Is the cafe correct? Give a reason.
5 marks
Show answer
a) 15, 50, 90, 110, 120b) 7.8 minutesc) Yes, 110 out of 120 = 91.7%
Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.