Week 6 · Stem-and-leaf plots: building single and double plots with a key and reading the median, the mode and the range from them · 3 lessons
1
Building a stem-and-leaf plot: splitting numbers into a stem and a leaf, ordering the leaves and writing the key
Statistics Sec 3 Term 1, Unit 2, Lesson 1
GoalBuild a stem-and-leaf plot from a list of whole numbers, order the leaves and write the key.
New words
stem · all the digits of a number except the last oneleaf · the last digit of a numberkey · a line that tells how to read one leaf, for example 2|3 = 23
Explanation
A list of numbers hides its shape. A stem-and-leaf plot keeps every value and also lets us see how the values are spread. Each number is cut in two parts: the last digit is the leaf, and all the digits in front of it are the stem. So 23 has stem 2 and leaf 3; 8 has stem 0 and leaf 8; 135 has stem 13 and leaf 5. To build the plot: (1) find the smallest and the largest stem and write every stem between them in a column, with a vertical line to its right; (2) write each leaf beside its stem, in the order of the list; (3) copy the plot again with the leaves in increasing order; a value that occurs twice gives two equal leaves; (4) write a key. The picture shows the minutes 16 pupils spent on a school bus trip (the data are invented).
key 2|3 = 23 minutes
Stem
Leaves
0
8 9
1
2 4 7 7 7
2
1 2 3 5 8
3
1 3 6
4
0
Worked examples
Splitting numbers. 23 = 2|3, 40 = 4|0, 8 = 0|8 (the stem is 0 because nothing stands in front of the 8). Whatever the number, the leaf is only one digit.
key 6|3 = 63 marks
Stem
Leaves
5
2 7 8
6
1 3 4 7 9
7
8
1 5 8
9
0
A gap is kept. Twelve marks out of 100 run from 52 to 90, and no mark lies in the seventies. We still write the stem 7 with no leaves: the gap is part of the picture. The 12 values are 52, 57, 58, 61, 63, 64, 67, 69, 81, 85, 88 and 90.
key 10|5 = 105 cm
Stem
Leaves
9
8 9
10
5 5 7
11
2 8
12
0 2
13
1
Three-digit numbers. The lengths of ten pieces of cloth in centimetres: 105, 98, 112, 120, 99, 107, 131, 118, 105, 122. Here 105 = 10|5, and 98 = 9|8. The stems run from 9 to 13.
Class activity
Ask 12 classmates how many minutes they need to get to school. Write the 12 numbers, build the plot with a key, and say which stem holds most leaves.
Practice
1
Write the stem and the leaf of 57, 6, 120 and 94.
57 = 5|7, 6 = 0|6, 120 = 12|0, 94 = 9|4.
2
Build an ordered plot for 34, 29, 41, 38, 29, 45. Write the key.
