Page 188 - MAT KS3 Y8 Cambridge CheckPoint

18.4 Interpreting and drawing stem-and-leaf diagrams

18.4 Interpreting and drawing stem-and-leaf diagrams

A stem-and-leaf diagram is a way of showing data in order of size. Key: 2 3 means 23 cm
When you draw a stem-and-leaf diagram, make sure that: 2 3 4 7 8
3 0 6 7 7 8
r you write the numbers in order of size from smallest to largest
r you write a key to explain the numbers 4 1 9 9
r you keep all the numbers in line vertically and horizontally.
stem leaves
Worked example 18.4

Here are the temperatures, in °C, recorded in 9 19 26 35 6 17 32 20 30 16
20 cities on one day.
14 16 18 29 27 8 25 32 20 32
a Draw an ordered stem-and-leaf diagram to show this
data.
‘Ordered’ means you write the
b How many cities had a temperature over 28°C?
c Use the stem-and-leaf diagram to work out: numbers in order of size from
i the mode ii the median iii the range of the data. smallest to largest.

a Unordered stem-and-leaf diagram
Key: 1 | 9 means 19°C Start by writing a key. You can use any of the numbers to explain the key.
Write in the stem numbers. In this case they are the tens digits, 0, 1, 2
0 968
and 3.
1 976468 Now write in the leaves, taking the numbers from the table above. So 9
has a stem of 0 and 9 as the leaf. 19 has a stem of 1 and 9 as the leaf.
2 609750
26 has a stem of 2 and 6 is the leaf. Complete for all 20 temperatures.
3 52022
Ordered stem-and-leaf diagram
Key: 1 | 9 means 19°C Now rewrite the diagram with all the leaves in order, from the smallest to
the biggest.
0 689
Make sure the stem numbers are in line vertically and that the leaves are in
1 466789 line vertically and horizontally.
2 005679

3 02225

b 6 cities You can see that 29 °C, 30 °C, 32 °C, 32 °C, 32 °C and 35 °C are all over 28 °C.
c i mode = 32 °C You can see that 32°C is the temperature that appears most often.
ii median = 20 °C There are 20 temperatures, so the median temperature is the average of
the 10th and 11th. These are both 20 °C, so the median is 20 °C.
iii range = 35 − 6 = 29 °C You can easily see from the diagram that the highest temperature is 35 °C
and the lowest is 6 °C. Subtract them to find the range.

✦ Exercise 18.4

1 Shen listed the playing times, to the nearest minute, of some CDs. Key: 4 5 means 45 minutes
He recorded the results in a stem-and-leaf diagram. 4 5 5 7 9
a How many CDs did Shen list? 5 0 2 5 6 8 9
b What is the shortest playing time? 6 1 2 4 6 7
c How many of the CDs had a playing time longer than 60 minutes?
d Work out:
i the mode ii the median iii the range of the data.
186 18 Interpreting and discussing results