Stem and Leaf Diagrams - Worksheets, Questions and Revision

17 original exam-style questions - 13 pages of questions with a full mark scheme - free printable PDF.

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GCSE · Statistics

S24 Stem and Leaf Diagrams

EDEXCEL 1ST0 · Calculator allowed · about 75 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Priya recorded the ages, in years, of 11 people at a Saturday book club. The stem-and-leaf diagram shows her results.
StemLeaf12325900368147Key: 2 | 3 means 23 years old
(a)Using the key, write down the age represented by the entry 3 | 1.(1)
(b)Write down the modal age.(1)
(c)Write down the number of people aged 30 or over.(1)
(d)Work out the range of the ages.(2)
(Total for Question 1 is 5 marks)
2
In a stem-and-leaf diagram of match attendances (stem = hundreds of spectators, so a leaf of 3 in the stem 4 row represents 430 spectators), the entry 6 | 8 represents an attendance of:
  • A) 680
  • B) 68
  • C) 6.8
  • D) 86
(Total for Question 2 is 1 mark)
3
The stem-and-leaf diagram shows the number of text messages sent in one day by each student in a small tutor group.
StemLeaf012377924481Key: 1 | 2 means 12 texts sent
(a)Write down the total number of students in the tutor group shown on the diagram.(1)
(b)Find the median number of texts sent.(2)
(Total for Question 3 is 3 marks)
4
The number of emails received in one week by 13 office workers were:

21, 34, 18, 29, 34, 15, 40, 27, 33, 19, 22, 36, 41

Construct an ordered stem-and-leaf diagram to show this information. Use the tens digit as the stem. Include a key.
StemLeaf1234Key: _____ | _____ means _______________
(Total for Question 4 is 3 marks)
5
The stem-and-leaf diagram shows the number of books read in a year by each of 14 members of a library reading group.
StemLeaf01246679125580004Key: 1 | 2 means 12 books
(a)Write down the mode of the number of books read.(1)
(b)Write down the number of members who read at least 15 books.(2)
(Total for Question 5 is 3 marks)
6
Write down two advantages of showing raw data in a stem-and-leaf diagram, rather than as a plain list of numbers.
(Total for Question 6 is 2 marks)
7
The stem-and-leaf diagram shows the test scores, out of 50, of 10 students.
StemLeaf2342577136815Key: 3 | 1 means a score of 31
(a)Work out the range of the scores.(2)
(b)Find the median score.(2)
(Total for Question 7 is 4 marks)
8
Amir is planning a statistical investigation into how long Year 11 students spend on homework each week. He plans to collect data from a sample of students and process it using a stem-and-leaf diagram before interpreting the results.
(a)Give one reason why a stem-and-leaf diagram is a useful way to process this raw data, compared with leaving it as an unsorted list.(1)
(b)Amir collects these times, in hours, from 15 students:

3, 9, 12, 6, 17, 4, 10, 8, 19, 14, 4, 11, 9, 12, 5

Construct an ordered stem-and-leaf diagram for this data. Include a key.(3)
(c)Find the median time spent on homework.(2)
(d)Comment on what the shape of the diagram suggests about the distribution of homework times, and state whether the mean would be higher or lower than the median.(2)
(Total for Question 8 is 8 marks)
9
The stem-and-leaf diagram shows the distance, in km, driven by 12 delivery drivers in one week. Because the distances run into the hundreds, each leaf here is a two-digit number (the last two digits of the distance) and the stem is the first digit.
StemLeaf23051518273441455668122540Key: 3 | 12 means 312 km
(a)Using the key, write down the distance represented by the leaf 34 in the stem 2 row.(1)
(b)Find the median distance travelled.(2)
(c)Work out the range of the distances.(2)
(Total for Question 9 is 5 marks)
10
The stem-and-leaf diagram shows the 100m sprint times, in seconds, of 13 athletes. The stem is the whole number of seconds and the leaf is the first decimal place.
StemLeaf1112132558013369047Key: 12 | 3 means 12.3 seconds
(a)Find the median sprint time.(2)
(b)Write down the number of athletes with a time faster than 12.0 seconds.(1)
(c)Work out the range of the sprint times.(2)
(Total for Question 10 is 5 marks)
11
Class A's and Class B's test scores (out of 40) were recorded:

Class A: 18, 25, 31, 22, 29, 33, 15, 27, 36, 24, 30, 21

Class B: 12, 20, 24, 28, 33, 35, 19, 22, 26, 31, 38, 17

Construct a back-to-back stem-and-leaf diagram to compare the two classes. Use the tens digit as the stem, with Class A's leaves on the left and Class B's leaves on the right. Include a key for each side.
Class AStemClass B123Key (Class A): _____ | _____ means _______Key (Class B): _____ | _____ means _______
(Total for Question 11 is 4 marks)
12
The back-to-back stem-and-leaf diagram below shows the completed test scores (out of 40) for Class A and Class B from Question 11.
Class AStemClass B123852799754210246863101358Key (Class A): 2 | 1 means a score of 21 for Class AKey (Class B): 1 | 2 means a score of 12 for Class B
(a)Find the median score for Class A and the median score for Class B.(2)
(b)Work out the range of scores for Class A and the range of scores for Class B.(2)
(Total for Question 12 is 4 marks)
13
A gym manager claims: "Most members of Tuesday's fitness class are under 30 years old." The stem-and-leaf diagram shows the ages of the 16 people in the class.
StemLeaf123458924578913561472Key: 2 | 4 means 24 years old
(Total for Question 13 is 3 marks)
14
Using your answers to Question 12, and the shape of the back-to-back stem-and-leaf diagram, compare the distribution of test scores for Class A and Class B.
(Total for Question 14 is 3 marks)
15
The stem-and-leaf diagram shows the weekly petrol spend, in pounds (GBP), of 19 households.
StemLeaf2345672581358146924703692Key: 3 | 1 means a weekly spend of GBP 31
(a)Find the lower quartile of the weekly petrol spend.(2)
(b)Find the upper quartile of the weekly petrol spend.(2)
(c)Hence find the interquartile range of the weekly petrol spend.(1)
(Total for Question 15 is 5 marks)
16
A stem-and-leaf diagram shows the ages, in years, of 9 people at a craft workshop. Eight of the leaves are shown below; the ninth (in the stem 4 row) is smudged and cannot be read.
1 | 8 92 | 5 83 | 1 2 74 | 0 ?
Key: 3 | 1 means 31 years old

The mean age of all 9 people is exactly 31 years. Work out the missing age.
(Total for Question 16 is 3 marks)
17
The stem-and-leaf diagram shows the finishing times, in minutes, of 15 runners in a fun run. The stem is whole minutes and the leaf is the first decimal place.
StemLeaf2627282930313233353739315041628507428Key: 29 | 4 means 29.4 minutes
(a)Find the interquartile range of the finishing times.(3)
(b)Write down the range of the finishing times.(2)
(c)Describe the skew of the distribution shown by the diagram, and state the effect this would have on the mean compared with the median.(2)
(Total for Question 17 is 7 marks)
Mark scheme · S24 Stem and Leaf Diagrams

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17