☰ Year plan · Statistics

Stem-and-leaf plots

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
2

Decimals and two-digit stems: plots of times and marks, and reading the median, the mode, the range and counts from a plot

Statistics Sec 3 Term 1, Unit 2, Lesson 1
GoalPlot decimal numbers and numbers with two-digit stems, and read the median, the mode, the range and counts from the plot.
New words
median · the middle value of the ordered data (the mean of the two middle values when there is an even number of values)mode · the value that occurs most oftenrange · the largest value minus the smallest value
Explanation

The leaf is always the last digit, so its worth is one unit of the last place. In a plot of whole numbers a leaf is a one; for a number such as 14.2 the stem is the whole part 14 and the leaf is a tenth. The key always tells which. Because the leaves of every row are in order, the whole plot is an ordered list: read it row by row from the top. The median is the middle value when the number of values is odd, and the mean of the two middle values when it is even. The mode is the value whose leaf is repeated most in one row. The range is the largest value minus the smallest. A count such as “how many are at least 70” is the number of leaves from one row to the end. The picture shows 15 invented times, in seconds, for the 100 m race of a school sports day.

key 14|2 = 14.2 s
Stem (seconds)Leaves (tenths)
129
134 4 6 7 9
142 2 2 6 8
151 8
164
170
Worked examples
Reading the sprint plot. There are 15 values, so the median is the 8th. The rows 12 and 13 hold 1 + 5 = 6 leaves, so the 7th, 8th and 9th values are the three leaves 2 of the row 14: the median is 14.2 s. The mode is also 14.2 s (the leaf 2 is written three times in the row 14). The range is 17.0 − 12.9 = 4.1 s. Eleven runners took less than 15 s: the rows 12, 13 and 14 hold 1 + 5 + 5 leaves.
key 6|2 = 62 marks
StemLeaves
47 9
55 8 9
62 2 2 2 5 6 8
70 1 4 7
83
91
Two-digit stems and an even number of values. Eighteen invented quiz marks out of 100. The 9th value is 62 and the 10th is 65, so the median is (62 + 65) ÷ 2 = 63.5. The mode is 62 (four leaves in the row 6). The range is 91 − 47 = 44. Six pupils scored at least 70 and five scored under 60.
key 5|1 = 5.1 kg
Stem (kg)Leaves (tenths)
42 2 6 8 9
51 1 1 5 9
63
70
Tenths as leaves. The masses of 12 watermelons in kilograms: 4.2, 5.1, 4.8, 6.3, 5.5, 4.2, 5.9, 4.9, 5.1, 7.0, 5.1, 4.6. The median is the mean of the 6th and 7th values: (5.1 + 5.1) ÷ 2 = 5.1 kg. The mode is 5.1 kg (three times). The range is 7.0 − 4.2 = 2.8 kg.
Class activity

Measure the hand spans of ten classmates in centimetres, to the nearest tenth. Plot the ten decimals with a key, then find the median, the mode (if there is one) and the range.

Practice
1
A plot has the key 3|5 = 3.5 m. Which numbers are in the row 4 | 0 7?
2
How many runners in the sprint plot took more than 14.2 s?
3
Data: 35, 42, 38, 47, 35, 51, 44. Plot them and find the median.
4
How many of the 12 watermelons weigh less than 5 kg?
5
Why is the median of an 18-value plot not one leaf but the mean of two values?