L4 · Stem-and-Leaf Plots

Learning goal

“I can read a stem-and-leaf plot using its key, list every value it shows, build one from raw data, and find the mode - and I can prove no data point is missing by counting the leaves.”

Stem — the first part of each value in a stem-and-leaf plot. For the two-digit values in this lesson, the stem is the tens digit.

Leaf — the last digit of each value. In this lesson, the leaf is the ones digit. Each leaf is one data point.

Key — the example that explains how to read the plot, such as "2|3 means 23." Always read the key first.

Stem-and-leaf plot — a representation that splits each value into a stem and a leaf, so the data is organized and every original value can still be read back.

Worked example

Eleven students recorded how many pages they read in one evening. The stem-and-leaf plot is: Stem 1 | leaves 2 5 5 8; Stem 2 | leaves 0 3 3 7; Stem 3 | leaves 1 4; Stem 4 | leaf 0. Key: 2|3 means 23 pages. Step 1: Read the KEY first: 2|3 means 23 - the stem is the tens digit, the leaf is the ones digit. Step 2: Read each row. Row 1 (stem 1): 12, 15, 15, 18. Row 2 (stem 2): 20, 23, 23, 27. Row 3 (stem 3): 31, 34. Row 4 (stem 4): 40. Step 3: The full ordered list is: 12, 15, 15, 18, 20, 23, 23, 27, 31, 34, 40. Step 4: CHECK by counting leaves: 4 + 4 + 2 + 1 = 11 leaves, and 11 students were surveyed. The number of leaves always equals the number of data points. Say it plainly: a leaf is not a value by itself. Stem and leaf together make the number - 2|3 is twenty-three, never "two and three."

Check yourself — explain it

In 2|3, why does the 2 stand for twenty and not for two?

Paired problem — example still visible

The ages of 7 cousins are shown in this plot: Stem 0 | leaves 5 7 9; Stem 1 | leaves 0 2 2 6. Key: 1|2 means 12 years old. List all the ages. How many cousins are there? What is the mode age? -> Ages: 5, 7, 9, 10, 12, 12, 16. There are 7 cousins (7 leaves). Mode: 12 (two leaves in the stem-1 row)

Faded completion — last step is yours

"Seedling heights (cm) are plotted below. One leaf is missing. Stem 2 | leaves 1 4 4 __; Stem 3 | leaves 0 3. Key: 2|4 means 24 cm. The missing height is 29 cm, so the missing leaf is ___. The values in the first row are 21, 24, 24, ___. When the leaf is filled in, the plot will show ___ values in all." -> 9; 29; 6

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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