Construct an ordered stem plot from raw data

The key is 4 | 0 means 4.0 cm. What length does 4 | 7 represent?

The key is 2 | 6 means 2.6 cm. A recorded length changes from 2.6 cm to 3.0 cm. Predict its new stem and leaf

Move the new length to 3.0 cm, then 5.9 cm. Read its highlighted leaf, the key and the empty rows

At 5.9 cm, what happens to stem 3?

The key determines place value

A stem plot preserves individual recorded values. Its key tells you how to combine the leading digits and the final digit. Continuous measurements can be shown at their recorded precision

1. 1Stems List consecutive stems from the smallest to the largest
2. 2Leaves Use one final digit per observation, in ascending order. Retain repeats and zeroes
3. 3Meaning Use the same key and measurement units throughout
4. 4Audit Reconstruct every record and check the number of leaves against the raw list

How many recorded lengths are exactly 4.0 cm?

Read the key and count every leaf, including repeats and zeroes

For 6.1, 6.4, 6.4 and 6.9 cm, what is the third ordered leaf in stem 6?

Read the key and count every leaf, including repeats and zeroes

Which interior stem is empty in this plot?

Read the key and count every leaf, including repeats and zeroes

How many recorded lengths are represented in this new plot?

Read the key and count every leaf, including repeats and zeroes

What is the median recorded length, in centimetres?

Read the key and count every leaf, including repeats and zeroes

What is the range of these lengths, in centimetres?

Read the key and count every leaf, including repeats and zeroes

The key is 3 | 8 means 3.8 cm. A student writes stem 3 and leaf 38. What needs correcting?

A crowded stem 4 is split into L for leaves 0–4 and H for leaves 5–9. Where will 4.5 cm go?

Change the moving length from 4.4 cm to 4.5 cm. Compare the low and high rows, then try 4.9 cm

At 4.5 cm, which counts are correct?

How many observations are represented by this split plot?

Read the key and count every leaf, including repeats and zeroes

In this whole-number plot, what length does stem 12 and leaf 8 represent, in centimetres?

Read the key and count every leaf, including repeats and zeroes

Can a stem plot of measurements recorded to tenths reveal their exact original hundredth-centimetre readings?

The raw list has twelve observations but the plot has eleven leaves. What is the best check?

Construct one complete plot

Draw an ordered plot for the recorded lengths 2.4, 1.8, 3.1, 2.4, 4.0, 3.6, 1.5 and 4.0 cm. Include a key and retain all eight observations. Compare your completed drawing with the worked example below. The following automatic questions grade their named entries; a complete drawing needs self or teacher review

1. 1Check Every source record must appear exactly once, including both 2.4s and both 4.0s
2. 2Choose and use technology Use a stem-plot function or a spreadsheet sort-and-split workflow to produce the same complete ordered plot. Explain your function choice. Record the input, place-value key, sorting direction, stem/leaf calculation and repeated/zero leaves. Do not assume a software default uses the required tenths key
3. 3Verify independently Decode every plotted stem/leaf pair back into a recorded value and match the complete sorted list to the source, including duplicates. Check the sample count and the key independently. Save your drawing and tool record before continuing; external-tool operation and the complete drawing are not automatically marked

Model response: preserve the key and every leaf

For the recorded lengths 2.4, 1.8, 3.1, 2.4, 4.0, 3.6, 1.5 and 4.0 cm, this tool record reproduces the complete ordered plot while keeping all eight observations

1. 1One reproducible workflow Enter raw lengths in A2:A9, sort them numerically in ascending order into B2:B9, then set C2=ROUND(10*B2,0), D2=QUOTIENT(C2,10), E2=MOD(C2,10) and fill down. C holds integer tenths, D stems and E single-digit leaves. Here all lengths are non-negative and recorded to tenths; multiplying by 10 preserves that precision. The rounding step removes possible machine representation residue, not an extra measurement digit
2. 2Assemble the complete plot Group leaves by consecutive stems 1, 2, 3, 4 while retaining ascending leaf order. The rows are 1 | 5 8, 2 | 4 4, 3 | 1 6, 4 | 0 0. Add the key “2 | 4 means 2.4 cm” and a title identifying recorded lengths. The spreadsheet columns are intermediate calculations; the final ordered rows and key are the required plot
3. 3Decode as an independent check Multiply each stem by ten, add its leaf, then divide by ten to recover 1.5, 1.8, 2.4, 2.4, 3.1, 3.6, 4.0, 4.0 cm, exactly the sorted source list. There are eight leaves, including two 4s in stem 2 and two zeroes in stem 4. A total of eight alone would not detect one wrong digit. Reading 2 | 4 as 24 cm would fail the key check by a factor of ten
4. 4Retain an empty stem when needed If a new length 6.2 cm is recorded, retain empty stem 5 and add 6 | 2. An empty row means no observations in that stem; a zero leaf would instead invent a recorded value of 5.0 cm. The sample count would become nine
5. 5Self-review Check the actual plot, group headings/key/units, consecutive stems, ordered single-digit leaves, repeats, zeroes, the decoded source match and your reproducible tool record. Do not extrapolate these formulas to negative values or a different precision without adapting the representation. The tool choice and independent drawing remain self or teacher reviewed

Why does the last row of this completed plot contain two zero leaves?