Worked examples
The question
Question: make a stem-and-leaf plot of 23, 31, 27, 45, 38, 22, 41 and 35.
Find the median.
23, 31, 27, 45, 38, 22, 41, 35
1 Split the numbers
The tens digit is the stem.
The ones digit is the leaf.
23: stem 2, leaf 3.
23: stem 2, leaf 3
Careful!
Every plot needs a key.
2, line, 3 means 23, not 5.
Careful: key: 2 | 3 means 23
2 Write the leaves
The stems go down the side: 2, 3 and 4.
23: leaf 3 goes after stem 2.
We cross out 23.
31: leaf 1 after stem 3.
And so on, in the order they come.
3 Put the leaves in order
Now we write the plot again, with each row of leaves in order, smallest first.
Stem 2: 2, 3 and 7.
And the key: 2, line, 3 means 23.
key: 2 | 3 = 23
4 Read the plot
The leaves are in order now.
We cross out the smallest and the biggest.
And the next pair, and so on.
Two are left in the middle: 31 and 35.
The median is halfway between them.
Halfway: we add them and divide by 2.
median = 31 + 352
31 plus 35 is 66.
Divided by 2 is 33.
So the median is 33.
median = 33
5 Check
Let's check: the plot has 8 leaves, one for each of the 8 numbers.
So none is lost!
3 + 3 + 2 = 8 leaves = 8 numbers
Let's look back.
First: split the numbers.
Then: write the leaves.
Then: put the leaves in order.
Then: read the plot.
Last: check.
▶ Watch it solved
The question
Question: make a stem-and-leaf plot of 56, 72, 64, 81, 59, 67, 75, 62, 70 and 68.
Find the median.
56, 72, 64, 81, 59, 67, 75, 62, 70, 68
1 Split the numbers
The tens digit is the stem.
The ones digit is the leaf.
56: stem 5, leaf 6.
56: stem 5, leaf 6
Careful!
Every plot needs a key.
5, line, 6 means 56, not 11.
Careful: key: 5 | 6 means 56
2 Write the leaves
The stems go down the side: 5, 6, 7 and 8.
56: leaf 6 goes after stem 5.
We cross out 56.
72: leaf 2 after stem 7.
And so on, in the order they come.
3 Put the leaves in order
Now we write the plot again, with each row of leaves in order, smallest first.
Stem 5: 6 and 9.
And the key: 5, line, 6 means 56.
key: 5 | 6 = 56
4 Read the plot
The leaves are in order now.
We cross out the smallest and the biggest.
And the next pair, and so on.
Two are left in the middle: 67 and 68.
The median is halfway between them.
Halfway: we add them and divide by 2.
median = 67 + 682
67 plus 68 is 135.
Divided by 2 is 67.5.
So the median is 67.5.
median = 67.5
5 Check
Let's check: the plot has 10 leaves, one for each of the 10 numbers.
So none is lost!
2 + 4 + 3 + 1 = 10 leaves = 10 numbers
Let's look back.
First: split the numbers.
Then: write the leaves.
Then: put the leaves in order.
Then: read the plot.
Last: check.
▶ Watch it solved
The question
Question: make a stem-and-leaf plot of 15, 28, 33, 21, 47, 19, 26, 35, 42, 24, 31, 17, 29 and 38.
Find the median.
15, 28, 33, 21, 47, 19, 26, 35, 42, 24, 31, 17, 29, 38
1 Split the numbers
The tens digit is the stem.
The ones digit is the leaf.
15: stem 1, leaf 5.
15: stem 1, leaf 5
Careful!
Every plot needs a key.
1, line, 5 means 15, not 6.
Careful: key: 1 | 5 means 15
2 Write the leaves
The stems go down the side: 1, 2, 3 and 4.
15: leaf 5 goes after stem 1.
We cross out 15.
28: leaf 8 after stem 2.
And so on, in the order they come.
3 Put the leaves in order
Now we write the plot again, with each row of leaves in order, smallest first.
Stem 1: 5, 7 and 9.
And the key: 1, line, 5 means 15.
key: 1 | 5 = 15
4 Read the plot
The leaves are in order now.
We cross out the smallest and the biggest.
And the next pair, and so on.
Two are left in the middle: 28 and 29.
The median is halfway between them.
Halfway: we add them and divide by 2.
median = 28 + 292
28 plus 29 is 57.
Divided by 2 is 28.5.
So the median is 28.5.
median = 28.5
5 Check
Let's check: the plot has 14 leaves, one for each of the 14 numbers.
So none is lost!
3 + 5 + 4 + 2 = 14 leaves = 14 numbers
Let's look back.
First: split the numbers.
Then: write the leaves.
Then: put the leaves in order.
Then: read the plot.
Last: check.
▶ Watch it solved
