Stem and leaf diagrams

1
Stem and leaf diagrams
2
Introduction

• Stem and leaf diagrams are used to
• retain raw data values (possibly rounded)
• provide a diagrammatic representation of the
  distribution - like bar chart
• find median, quartiles etc

3
Stages in drawing a stem and leaf

• Decide on and provide a key for the stem and
  leaf. The leaf is always the smallest (least
  significant) digit - you may need to round in
  some circumstances
• Draw a preliminary stem and leaf directly from
  the raw data - this is likely to mean the leafs
  are unordered
• Draw a new stem and leaf diagram with the leaves
  put into numerical order.
• If needed add the number of leaves

4
Example - drawing a stem and leaf
Question- 29 students were set a simple
task. Their completion times to the nearest
second were 47 61 53 43 46 46 68 48 72
57 48 54 41 63 49 42 58 65 45 44 43
51 45 38 46 44 52 43 47 (a) set these
data into a stem and leaf diagram (b) find the
median, quartiles and inter-quartile range
Answer (a)- (1) key 47 means 47 (2) put
values into preliminary diagram

stem
leaf
5
Example - drawing a stem and leaf
Question- 29 students were set a simple
task. Their completion times to the nearest
second were 47 61 53 43 46 46 68 48 72
57 48 54 41 63 49 42 58 65 45 44 43
51 45 38 46 44 52 43 47 (a) set these
data into a stem and leaf diagram (b) find the
median, quartiles and inter-quartile range
Answer (a)- (1) key 47 means 47 (2) put
values into preliminary diagram
Completion times
3 4 5 6 7
7
6
Example - drawing a stem and leaf
Question- 29 students were set a simple
task. Their completion times to the nearest
second were 47 61 53 43 46 46 68 48 72
57 48 54 41 63 49 42 58 65 45 44 43
51 45 38 46 44 52 43 47 (a) set these
data into a stem and leaf diagram (b) find the
median, quartiles and inter-quartile range
Answer (a)- (1) key 47 means 47 (2) put
values into preliminary diagram
Completion times
3 4 5 6 7
7 1
7
Example - drawing a stem and leaf
Question- 29 students were set a simple
task. Their completion times to the nearest
second were 47 61 53 43 46 46 68 48 72
57 48 54 41 63 49 42 58 65 45 44 43
51 45 38 46 44 52 43 47 (a) set these
data into a stem and leaf diagram (b) find the
median, quartiles and inter-quartile range
Answer (a)- (1) key 47 means 47 (2) put
values into preliminary diagram
Completion times
3 4 5 6 7
7 3 1
8
Example - drawing a stem and leaf
Question- 29 students were set a simple
task. Their completion times to the nearest
second were 47 61 53 43 46 46 68 48 72
57 48 54 41 63 49 42 58 65 45 44 43
51 45 38 46 44 52 43 47 (a) set these
data into a stem and leaf diagram (b) find the
median, quartiles and inter-quartile range
Answer (a)- (1) key 47 means 47 (2) put
values into preliminary diagram
Completion times
3 4 5 6 7
7 3 3 1
9
Example - drawing a stem and leaf
Question- 29 students were set a simple
task. Their completion times to the nearest
second were 47 61 53 43 46 46 68 48 72
57 48 54 41 63 49 42 58 65 45 44 43
51 45 38 46 44 52 43 47 (a) set these
data into a stem and leaf diagram (b) find the
median, quartiles and inter-quartile range
Answer (a)- (1) key 47 means 47 (2) put
values into preliminary diagram
Completion times
3 4 5 6 7
7 3 6 3 1
10
Example - drawing a stem and leaf
Question- 29 students were set a simple
task. Their completion times to the nearest
second were 47 61 53 43 46 46 68 48 72
57 48 54 41 63 49 42 58 65 45 44 43
51 45 38 46 44 52 43 47 (a) set these
data into a stem and leaf diagram (b) find the
median, quartiles and inter-quartile range
Answer (a)- (1) key 47 means 47 (2) put
values into preliminary diagram
Completion times
3 4 5 6 7
7 3 6 6 3 1
11
Example - drawing a stem and leaf
Question- 29 students were set a simple
task. Their completion times to the nearest
second were 47 61 53 43 46 46 68 48 72
57 48 54 41 63 49 42 58 65 45 44 43
51 45 38 46 44 52 43 47 (a) set these
data into a stem and leaf diagram (b) find the
median, quartiles and inter-quartile range
Answer (a)- (1) key 47 means 47 (2) put
values into preliminary diagram
Completion times
3 4 5 6 7
7 3 6 6 3 1 8
12
Example - drawing a stem and leaf
Question- 29 students were set a simple
task. Their completion times to the nearest
second were 47 61 53 43 46 46 68 48 72
57 48 54 41 63 49 42 58 65 45 44 43
51 45 38 46 44 52 43 47 (a) set these
data into a stem and leaf diagram (b) find the
median, quartiles and inter-quartile range
Answer (a)- (1) key 47 means 47 (2) put
values into preliminary diagram
Completion times
3 4 5 6 7
7 3 6 6 8 3 1 8
13
Example - drawing a stem and leaf
Question- 29 students were set a simple
task. Their completion times to the nearest
second were 47 61 53 43 46 46 68 48 72
57 48 54 41 63 49 42 58 65 45 44 43
51 45 38 46 44 52 43 47 (a) set these
data into a stem and leaf diagram (b) find the
median, quartiles and inter-quartile range
Answer (a)- (1) key 47 means 47 (2) put
values into preliminary diagram
Completion times
3 4 5 6 7
7 3 6 6 8 3 1 8 2
14
Example - drawing a stem and leaf
Question- 29 students were set a simple
task. Their completion times to the nearest
second were 47 61 53 43 46 46 68 48 72
57 48 54 41 63 49 42 58 65 45 44 43
51 45 38 46 44 52 43 47 (a) set these
data into a stem and leaf diagram (b) find the
median, quartiles and inter-quartile range
Answer (a)- (1) key 47 means 47 (2) put
values into preliminary diagram
Completion times
3 4 5 6 7
7 3 6 6 8 3 7 1 8 2
15
Example - drawing a stem and leaf
Question- 29 students were set a simple
task. Their completion times to the nearest
second were 47 61 53 43 46 46 68 48 72
57 48 54 41 63 49 42 58 65 45 44 43
51 45 38 46 44 52 43 47 (a) set these
data into a stem and leaf diagram (b) find the
median, quartiles and inter-quartile range
Answer (a)- (1) key 47 means 47 (2) put
values into preliminary diagram
Completion times
3 4 5 6 7
7 3 6 6 8 8 3 7 1 8 2
16
Example - drawing a stem and leaf
Question- 29 students were set a simple
task. Their completion times to the nearest
second were 47 61 53 43 46 46 68 48 72
57 48 54 41 63 49 42 58 65 45 44 43
51 45 38 46 44 52 43 47 (a) set these
data into a stem and leaf diagram (b) find the
median, quartiles and inter-quartile range
Answer (a)- (1) key 47 means 47 (2) put
values into preliminary diagram
Completion times
3 4 5 6 7
7 3 6 6 8 8 3 7 4 1 8 2
17
Example - drawing a stem and leaf
Question- 29 students were set a simple
task. Their completion times to the nearest
second were 47 61 53 43 46 46 68 48 72
57 48 54 41 63 49 42 58 65 45 44 43
51 45 38 46 44 52 43 47 (a) set these
data into a stem and leaf diagram (b) find the
median, quartiles and inter-quartile range
Answer (a)- (1) key 47 means 47 (2) put
values into preliminary diagram
Completion times
3 4 5 6 7
7 3 6 6 8 8 1 3 7 4 1 8 2
18
Example - drawing a stem and leaf
Question- 29 students were set a simple
task. Their completion times to the nearest
second were 47 61 53 43 46 46 68 48 72
57 48 54 41 63 49 42 58 65 45 44 43
51 45 38 46 44 52 43 47 (a) set these
data into a stem and leaf diagram (b) find the
median, quartiles and inter-quartile range
Answer (a)- (1) key 47 means 47 (2) put
values into preliminary diagram
Completion times
3 4 5 6 7
7 3 6 6 8 8 1 3 7 4 1 8 3 2
19
Example - drawing a stem and leaf
Question- 29 students were set a simple
task. Their completion times to the nearest
second were 47 61 53 43 46 46 68 48 72
57 48 54 41 63 49 42 58 65 45 44 43
51 45 38 46 44 52 43 47 (a) set these
data into a stem and leaf diagram (b) find the
median, quartiles and inter-quartile range
Answer (a)- (1) key 47 means 47 (2) put
values into preliminary diagram
Completion times
3 4 5 6 7
7 3 6 6 8 8 1 9 3 7 4 1 8 3 2
20
Example - drawing a stem and leaf
Question- 29 students were set a simple
task. Their completion times to the nearest
second were 47 61 53 43 46 46 68 48 72
57 48 54 41 63 49 42 58 65 45 44 43
51 45 38 46 44 52 43 47 (a) set these
data into a stem and leaf diagram (b) find the
median, quartiles and inter-quartile range
Answer (a)- (1) key 47 means 47 (2) put
values into preliminary diagram
Completion times
3 4 5 6 7
7 3 6 6 8 8 1 9 2 3 7 4 1 8 3 2
21
Example - drawing a stem and leaf
Question- 29 students were set a simple
task. Their completion times to the nearest
second were 47 61 53 43 46 46 68 48 72
57 48 54 41 63 49 42 58 65 45 44 43
51 45 38 46 44 52 43 47 (a) set these
data into a stem and leaf diagram (b) find the
median, quartiles and inter-quartile range
Answer (a)- (1) key 47 means 47 (2) put
values into preliminary diagram
Completion times
3 4 5 6 7
7 3 6 6 8 8 1 9 2 3 7 4 8 1 8 3 2
22
Example - drawing a stem and leaf
Question- 29 students were set a simple
task. Their completion times to the nearest
second were 47 61 53 43 46 46 68 48 72
57 48 54 41 63 49 42 58 65 45 44 43
51 45 38 46 44 52 43 47 (a) set these
data into a stem and leaf diagram (b) find the
median, quartiles and inter-quartile range
Answer (a)- (1) key 47 means 47 (2) put
values into preliminary diagram
Completion times
3 4 5 6 7
7 3 6 6 8 8 1 9 2 3 7 4 8 1 8 3
5 2
23
Example - drawing a stem and leaf
Question- 29 students were set a simple
task. Their completion times to the nearest
second were 47 61 53 43 46 46 68 48 72
57 48 54 41 63 49 42 58 65 45 44 43
51 45 38 46 44 52 43 47 (a) set these
data into a stem and leaf diagram (b) find the
median, quartiles and inter-quartile range
Answer (a)- (1) key 47 means 47 (2) put
values into preliminary diagram
Completion times
3 4 5 6 7
7 3 6 6 8 8 1 9 2 5 3 7 4 8 1 8
3 5 2
24
Example - drawing a stem and leaf
Question- 29 students were set a simple
task. Their completion times to the nearest
second were 47 61 53 43 46 46 68 48 72
57 48 54 41 63 49 42 58 65 45 44 43
51 45 38 46 44 52 43 47 (a) set these
data into a stem and leaf diagram (b) find the
median, quartiles and inter-quartile range
Answer (a)- (1) key 47 means 47 (2) put
values into preliminary diagram
Completion times
3 4 5 6 7
7 3 6 6 8 8 1 9 2 5 4 3 7 4 8 1
8 3 5 2
25
Example - drawing a stem and leaf
Question- 29 students were set a simple
task. Their completion times to the nearest
second were 47 61 53 43 46 46 68 48 72
57 48 54 41 63 49 42 58 65 45 44 43
51 45 38 46 44 52 43 47 (a) set these
data into a stem and leaf diagram (b) find the
median, quartiles and inter-quartile range
Answer (a)- (1) key 47 means 47 (2) put
values into preliminary diagram
Completion times
3 4 5 6 7
7 3 6 6 8 8 1 9 2 5 4 3 3 7 4
8 1 8 3 5 2
26
Example - drawing a stem and leaf
Question- 29 students were set a simple
task. Their completion times to the nearest
second were 47 61 53 43 46 46 68 48 72
57 48 54 41 63 49 42 58 65 45 44 43
51 45 38 46 44 52 43 47 (a) set these
data into a stem and leaf diagram (b) find the
median, quartiles and inter-quartile range
Answer (a)- (1) key 47 means 47 (2) put
values into preliminary diagram
Completion times
3 4 5 6 7
7 3 6 6 8 8 1 9 2 5 4 3 3 7 4 8
1 1 8 3 5 2
27
Example - drawing a stem and leaf
Question- 29 students were set a simple
task. Their completion times to the nearest
second were 47 61 53 43 46 46 68 48 72
57 48 54 41 63 49 42 58 65 45 44 43
51 45 38 46 44 52 43 47 (a) set these
data into a stem and leaf diagram (b) find the
median, quartiles and inter-quartile range
Answer (a)- (1) key 47 means 47 (2) put
values into preliminary diagram
Completion times
3 4 5 6 7
7 3 6 6 8 8 1 9 2 5 4 3 5 3 7 4
8 1 1 8 3 5 2
28
Example - drawing a stem and leaf
Question- 29 students were set a simple
task. Their completion times to the nearest
second were 47 61 53 43 46 46 68 48 72
57 48 54 41 63 49 42 58 65 45 44 43
51 45 38 46 44 52 43 47 (a) set these
data into a stem and leaf diagram (b) find the
median, quartiles and inter-quartile range
Answer (a)- (1) key 47 means 47 (2) put
values into preliminary diagram
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 3 7
4 8 1 1 8 3 5 2
29
Example - drawing a stem and leaf
Question- 29 students were set a simple
task. Their completion times to the nearest
second were 47 61 53 43 46 46 68 48 72
57 48 54 41 63 49 42 58 65 45 44 43
51 45 38 46 44 52 43 47 (a) set these
data into a stem and leaf diagram (b) find the
median, quartiles and inter-quartile range
Answer (a)- (1) key 47 means 47 (2) put
values into preliminary diagram
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 3
7 4 8 1 1 8 3 5 2
30
Example - drawing a stem and leaf
Question- 29 students were set a simple
task. Their completion times to the nearest
second were 47 61 53 43 46 46 68 48 72
57 48 54 41 63 49 42 58 65 45 44 43
51 45 38 46 44 52 43 47 (a) set these
data into a stem and leaf diagram (b) find the
median, quartiles and inter-quartile range
Answer (a)- (1) key 47 means 47 (2) put
values into preliminary diagram
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 4 8 1 1 8 3 5 2
31
Example - drawing a stem and leaf
Question- 29 students were set a simple
task. Their completion times to the nearest
second were 47 61 53 43 46 46 68 48 72
57 48 54 41 63 49 42 58 65 45 44 43
51 45 38 46 44 52 43 47 (a) set these
data into a stem and leaf diagram (b) find the
median, quartiles and inter-quartile range
Answer (a)- (1) key 47 means 47 (2) put
values into preliminary diagram
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4
3 7 4 8 1 2 1 8 3 5 2
32
Example - drawing a stem and leaf
Question- 29 students were set a simple
task. Their completion times to the nearest
second were 47 61 53 43 46 46 68 48 72
57 48 54 41 63 49 42 58 65 45 44 43
51 45 38 46 44 52 43 47 (a) set these
data into a stem and leaf diagram (b) find the
median, quartiles and inter-quartile range
Answer (a)- (1) key 47 means 47 (2) put
values into preliminary diagram
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
3 7 4 8 1 2 1 8 3 5 2
33
Example - drawing a stem and leaf
Question- 29 students were set a simple
task. Their completion times to the nearest
second were 47 61 53 43 46 46 68 48 72
57 48 54 41 63 49 42 58 65 45 44 43
51 45 38 46 44 52 43 47 (a) set these
data into a stem and leaf diagram (b) find the
median, quartiles and inter-quartile range
Answer (a)- (1) key 47 means 47 (2) put
values into preliminary diagram
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 3 7 4 8 1 2 1 8 3 5 2
34
Example - drawing a stem and leaf
Question- 29 students were set a simple
task. Their completion times to the nearest
second were 47 61 53 43 46 46 68 48 72
57 48 54 41 63 49 42 58 65 45 44 43
51 45 38 46 44 52 43 47 (a) set these
data into a stem and leaf diagram (b) find the
median, quartiles and inter-quartile range
Answer (a)- (1) key 47 means 47 (2) put
values into preliminary diagram
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 3 7 4 8 1 2 1 8 3 5 2
(3) re draw diagram with leafs in numerical
order
35
Example - drawing a stem and leaf
Answer (a)- (3) re draw diagram with leafs in
numerical order
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 3 7 4 8 1 2 1 8 3 5 2
Completion times
3 4 5 6 7

36
Example - drawing a stem and leaf
Answer (a)- (3) re draw diagram with leafs in
numerical order
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 3 7 4 8 1 2 1 8 3 5 2
Completion times
3 4 5 6 7
8
37
Example - drawing a stem and leaf
Answer (a)- (3) re draw diagram with leafs in
numerical order
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 3 7 4 8 1 2 1 8 3 5 2
Completion times
3 4 5 6 7
8 1
38
Example - drawing a stem and leaf
Answer (a)- (3) re draw diagram with leafs in
numerical order
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 3 7 4 8 1 2 1 8 3 5 2
Completion times
3 4 5 6 7
8 1 2
39
Example - drawing a stem and leaf
Answer (a)- (3) re draw diagram with leafs in
numerical order
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 3 7 4 8 1 2 1 8 3 5 2
Completion times
3 4 5 6 7
8 1 2 3
40
Example - drawing a stem and leaf
Answer (a)- (3) re draw diagram with leafs in
numerical order
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 3 7 4 8 1 2 1 8 3 5 2
Completion times
3 4 5 6 7
8 1 2 3 3
41
Example - drawing a stem and leaf
Answer (a)- (3) re draw diagram with leafs in
numerical order
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 3 7 4 8 1 2 1 8 3 5 2
Completion times
3 4 5 6 7
8 1 2 3 3 3
42
Example - drawing a stem and leaf
Answer (a)- (3) re draw diagram with leafs in
numerical order
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 3 7 4 8 1 2 1 8 3 5 2
Completion times
3 4 5 6 7
8 1 2 3 3 3 4
43
Example - drawing a stem and leaf
Answer (a)- (3) re draw diagram with leafs in
numerical order
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 3 7 4 8 1 2 1 8 3 5 2
Completion times
3 4 5 6 7
8 1 2 3 3 3 4 4
44
Example - drawing a stem and leaf
Answer (a)- (3) re draw diagram with leafs in
numerical order
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 3 7 4 8 1 2 1 8 3 5 2
Completion times
3 4 5 6 7
8 1 2 3 3 3 4 4 5
45
Example - drawing a stem and leaf
Answer (a)- (3) re draw diagram with leafs in
numerical order
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 3 7 4 8 1 2 1 8 3 5 2
Completion times
3 4 5 6 7
8 1 2 3 3 3 4 4 5 5
46
Example - drawing a stem and leaf
Answer (a)- (3) re draw diagram with leafs in
numerical order
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 3 7 4 8 1 2 1 8 3 5 2
Completion times
3 4 5 6 7
8 1 2 3 3 3 4 4 5 5 6
47
Example - drawing a stem and leaf
Answer (a)- (3) re draw diagram with leafs in
numerical order
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 3 7 4 8 1 2 1 8 3 5 2
Completion times
3 4 5 6 7
8 1 2 3 3 3 4 4 5 5 6 6
48
Example - drawing a stem and leaf
Answer (a)- (3) re draw diagram with leafs in
numerical order
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 3 7 4 8 1 2 1 8 3 5 2
Completion times
3 4 5 6 7
8 1 2 3 3 3 4 4 5 5 6 6 6
49
Example - drawing a stem and leaf
Answer (a)- (3) re draw diagram with leafs in
numerical order
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 3 7 4 8 1 2 1 8 3 5 2
Completion times
3 4 5 6 7
8 1 2 3 3 3 4 4 5 5 6 6 6 7
50
Example - drawing a stem and leaf
Answer (a)- (3) re draw diagram with leafs in
numerical order
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 3 7 4 8 1 2 1 8 3 5 2
Completion times
3 4 5 6 7
8 1 2 3 3 3 4 4 5 5 6 6 6 7 7
51
Example - drawing a stem and leaf
Answer (a)- (3) re draw diagram with leafs in
numerical order
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 3 7 4 8 1 2 1 8 3 5 2
Completion times
3 4 5 6 7
8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8
52
Example - drawing a stem and leaf
Answer (a)- (3) re draw diagram with leafs in
numerical order
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 3 7 4 8 1 2 1 8 3 5 2
Completion times
3 4 5 6 7
8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8
53
Example - drawing a stem and leaf
Answer (a)- (3) re draw diagram with leafs in
numerical order
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 3 7 4 8 1 2 1 8 3 5 2
Completion times
3 4 5 6 7
8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8
9
54
Example - drawing a stem and leaf
Answer (a)- (3) re draw diagram with leafs in
numerical order
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 3 7 4 8 1 2 1 8 3 5 2
Completion times
3 4 5 6 7
8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8
9 1
55
Example - drawing a stem and leaf
Answer (a)- (3) re draw diagram with leafs in
numerical order
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 3 7 4 8 1 2 1 8 3 5 2
Completion times
3 4 5 6 7
8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8
9 1 2
56
Example - drawing a stem and leaf
Answer (a)- (3) re draw diagram with leafs in
numerical order
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 3 7 4 8 1 2 1 8 3 5 2
Completion times
3 4 5 6 7
8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8
9 1 2 3
57
Example - drawing a stem and leaf
Answer (a)- (3) re draw diagram with leafs in
numerical order
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 3 7 4 8 1 2 1 8 3 5 2
Completion times
3 4 5 6 7
8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8
9 1 2 3 4
58
Example - drawing a stem and leaf
Answer (a)- (3) re draw diagram with leafs in
numerical order
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 3 7 4 8 1 2 1 8 3 5 2
Completion times
3 4 5 6 7
8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8
9 1 2 3 4 7
59
Example - drawing a stem and leaf
Answer (a)- (3) re draw diagram with leafs in
numerical order
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 3 7 4 8 1 2 1 8 3 5 2
Completion times
3 4 5 6 7
8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8
9 1 2 3 4 7 8
60
Example - drawing a stem and leaf
Answer (a)- (3) re draw diagram with leafs in
numerical order
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 3 7 4 8 1 2 1 8 3 5 2
Completion times
3 4 5 6 7

• 8
• 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9
• 1 2 3 4 7 8
• 1

61
Example - drawing a stem and leaf
Answer (a)- (3) re draw diagram with leafs in
numerical order
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 3 7 4 8 1 2 1 8 3 5 2
Completion times
3 4 5 6 7

• 8
• 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9
• 1 2 3 4 7 8
• 1 3

62
Example - drawing a stem and leaf
Answer (a)- (3) re draw diagram with leafs in
numerical order
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 3 7 4 8 1 2 1 8 3 5 2
Completion times
3 4 5 6 7

• 8
• 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9
• 1 2 3 4 7 8
• 1 3 5

63
Example - drawing a stem and leaf
Answer (a)- (3) re draw diagram with leafs in
numerical order
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 3 7 4 8 1 2 1 8 3 5 2
Completion times
3 4 5 6 7

• 8
• 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9
• 1 2 3 4 7 8
• 1 3 5 8

64
Example - drawing a stem and leaf
Answer (a)- (3) re draw diagram with leafs in
numerical order
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 3 7 4 8 1 2 1 8 3 5 2
Dont forget the key
Completion times
47 means 47
3 4 5 6 7
8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8
9 1 2 3 4 7 8 1 3 5 8 2
65
Example - drawing a stem and leaf
Question- 29 students were set a simple
task. Their completion times to the nearest
second were 47 61 53 43 46 46 68 48 72
57 48 54 41 63 49 42 58 65 45 44 43
51 45 38 46 44 52 43 47 (a) set these
data into a stem and leaf diagram (b) find the
median, quartiles and inter-quartile range
Answer (b)- adding the number of leaves can be
helpful when interpreting a diagram
Completion times
3 4 5 6 7
8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8
9 1 2 3 4 7 8 1 3 5 8 2
(1) (17) (6) (4) (1)
66
Example - drawing a stem and leaf
Answer (b)- find the median, quartiles and
inter-quartile range
Completion times
3 4 5 6 7
8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8
9 1 2 3 4 7 8 1 3 5 8 2
(1) (17) (6) (4) (1)
The median is the middle value
n/2 29/2 14.5
? 15th value
Not whole - so round up
to whole
Find the 15th value
67
Example - drawing a stem and leaf
Answer (b)- find the median, quartiles and
inter-quartile range
Completion times
3 4 5 6 7
8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8
9 1 2 3 4 7 8 1 3 5 8 2
(1) (17) (6) (4) (1)
The median is the middle value
n/2 29/2 14.5
? 15th value
47 seconds
Not whole - so round up
to whole
Find the 15th value
68
Example - drawing a stem and leaf
Answer (b)- find the median, quartiles and
inter-quartile range
Completion times
3 4 5 6 7
8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8
9 1 2 3 4 7 8 1 3 5 8 2
(1) (17) (6) (4) (1)
The median is the middle value
n/2 29/2 14.5
? 15th value
47 seconds
The lower quartile, Q1, is the 1/4th value
n/4 29/4 7.25
? 8th value
not whole - so round up
to whole
69
Example - drawing a stem and leaf
Answer (b)- find the median, quartiles and
inter-quartile range
Completion times
3 4 5 6 7
8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8
9 1 2 3 4 7 8 1 3 5 8 2
(1) (17) (6) (4) (1)
The median is the middle value
n/2 29/2 14.5
? 15th value
47 seconds
The lower quartile, Q1, is the 1/4th value
n/4 29/4 7.25
? 8th value
44 seconds
not whole - so round up
to whole
70
Example - drawing a stem and leaf
Answer (b)- find the median, quartiles and
inter-quartile range
Completion times
3 4 5 6 7
8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8
9 1 2 3 4 7 8 1 3 5 8 2
(1) (17) (6) (4) (1)
The median is the middle value
n/2 29/2 14.5
? 15th value
47 seconds
The lower quartile, Q1, is the 1/4th value
n/4 29/4 7.25
44 seconds
? 8th value
The upper quartile, Q3, is the 3/4th value
3n/4 3x29/4 21.75
? 22nd value
not whole - so round up
to whole
71
Example - drawing a stem and leaf
Answer (b)- find the median, quartiles and
inter-quartile range
Completion times
3 4 5 6 7
8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8
9 1 2 3 4 7 8 1 3 5 8 2
(1) (17) (6) (4) (1)
The median is the middle value
n/2 29/2 14.5
? 15th value
47 seconds
The lower quartile, Q1, is the 1/4th value
n/4 29/4 7.25
44 seconds
? 8th value
The upper quartile, Q3, is the 3/4th value
3n/4 3x29/4 21.75
? 22nd value
54 seconds
not whole -so round up
to whole
72
Example - drawing a stem and leaf
Answer (b)- find the median, quartiles and
inter-quartile range
Completion times
3 4 5 6 7
8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8
9 1 2 3 4 7 8 1 3 5 8 2
(1) (17) (6) (4) (1)
The median is the middle value
n/2 29/2 14.5
? 15th value
47 seconds
The lower quartile, Q1, is the 1/4th value
n/4 29/4 7.25
44 seconds
? 8th value
The upper quartile, Q3, is the 3/4th value
3n/4 3x29/4 21.75
? 22nd value
54 seconds
The inter quartile range Q3 Q1 54 44 10
seconds
73
Note

• you are more likely to be required to interpret a
  stem and leaf diagram than to have to draw one
• the textbook examples use a stem consisting of
  one digit. More digits are possible.
• The range of values should not be too great -
  otherwise the values may need to be rounded so
  that the number of stems does not become too
  large
• Stem and leaf diagrams can be drawn back to back
  for comparisons much like bar charts.