--- title: "Stem-and-leaf plots" subtitle: "Data and chance · Data · Lesson 4" --- # Stem-and-leaf plots **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** Thirty homework times in a list tell you very little. Sort them into a stem-and-leaf plot and the shape jumps out, and you can still read every value. :::teacher-note **In one sentence:** Students build ordered stem-and-leaf plots (tens as stems, units as leaves, every stem included, with a key) and read values, the median, mode and range from them (AC9M7ST02, node 1). **Students should be able to say:** I can build an ordered stem-and-leaf plot with a key. I can read values, the median, the mode and the range from a stem-and-leaf plot. **Width:** the unmarked parts are the floor every student does (predict, run, investigate and make). Typical adds the modify practice; wider adds the real-world contexts. They add contexts, not difficulty. Students work in the online tutorial alongside this sheet. ::: ## Predict How many values are in that row? :::keep-together **In a stem-and-leaf plot, a row reads $3 \mid 1\ 5\ 5\ 8$. Which values does it show?** ☐ 31, 35, 35 and 38 ☐ The number 31 558 ☐ 3, 1, 5, 5 and 8 ☐ 3, 15 and 58 My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** 31, 35, 35 and 38. The stem 3 is the tens; each leaf is the units of one value. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Build and read :::keep-together ### Build, then read Here is how to build one, and read from it. 1. $23, 31, 35, 35, 38, 42, 47, 51$ — Sort the values first (or sort the leaves at the end). 2. $\text{stems: } 2, 3, 4, 5$ — The tens digits, from smallest to largest, none missed out. 3. $3 \mid 1\ 5\ 5\ 8$ — Each value's units digit goes on its stem's row, in order. 4. $\text{Key: } 3 \mid 5 = 35$ — A key says how to read the plot. 5. $\text{median} = \tfrac{35 + 38}{2} = 36.5$ — 8 values: count in to the 4th and 5th leaves. Now read the median of the plot in the picture. **What is the median of the data in this plot?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 27 11 values, so the median is the 6th: 14, 18, 21, 23, 23, 27. ::: :::keep-together ### Find the mistake **Jo draws a stem-and-leaf plot. Click the line where her working goes wrong.** ``` 1 Values: 12, 15, 21, 27, 43, 48. 2 The stems are the tens digits. 3 Write the stems that have values: 1, 2, 4. 4 Leaves: 1 | 2 5, 2 | 1 7, 4 | 3 8. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 3 Line 3: every stem from the smallest to the largest goes in, even with no leaves: 1, 2, 3, 4. The empty 3 row shows the gap between the 20s and the 40s. ::: :::keep-together ### Range from the plot **What is the range of the data?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 31 Highest 45, lowest 14: 45 − 14 = 31. ::: :::typical ## One change at a time **Build one.** Each task changes one thing. **The mode.** **Count the values.** **Use the key.** **Three digits.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Read the plot :::keep-together ### Median **What is the median?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 63 5th and 6th values are both 63, so the median is 63. ::: :::keep-together ### Range **What is the range?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 27 79 − 52 = 27. ::: :::keep-together ### Which stems **Values $41, 44, 62, 65$. Which stems should the plot have?** ☐ 4 and 6 ☐ 1, 2, 4 and 5 ☐ 4, 5 and 6 (5 has no leaves) ::: :::teacher-note **Answer:** 4, 5 and 6 (5 has no leaves) Every stem from 4 to 6, so the empty 5 row shows the gap. ::: :::keep-together ### Review: mean **Review: find the mean of $23, 31, 35, 35$.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 31 124 ÷ 4 = 31. ::: ## Make: a plot with a given median Then: could you do it with no value of 35 at all? Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **Draw a stem-and-leaf plot of 17, 25, 22, 41, 18, 29, 26 and find its median.** {{lines-3}} ::: :::teacher-note **Answer:** 1 | 7 8, 2 | 2 5 6 9, 3 | (empty), 4 | 1. Median: the 4th of 7 values, 25. :::