Stem and Leaf Plot Worksheets - Free Printable

Let’s solve each part step by step.

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Problem 1: Coffee cups sold in two weeks

Stem-and-leaf plot key:
`5 | 2 = 72 cups` → So stem is tens digit, leaf is ones digit. But wait — the key says “5 | 2 = 72”, which means we add 50 + 2? No — that doesn’t make sense. Actually, looking again: if 5 | 2 = 72, then maybe it's stem × 10 + leaf + something? Wait — let’s check:

Actually, re-read the key:
> Key: `5 | 2 = 72 cups`

That suggests:
Stem “5” and leaf “2” together represent 72.
So perhaps: (stem + 5) × 10 + leaf? Let’s test:
If stem=5, leaf=2 → (5+5)*10 + 2 = 10*10 + 2 = 102 → no.

Wait — maybe it’s just a typo or misprint? Or perhaps the key means:
The number is formed as: tens digit from stem, ones from leaf, but the example is wrong? That can’t be.

Wait — look at the data:

Sales row:
```
5 | 2 8 9
6 | 3 4 6 8
7 | 1 5 7 8
```

And key: `5 | 2 = 72`

Ah! Maybe the stem represents 70s, 60s, etc.? No.

Alternative idea: Perhaps the key is saying that the value is stem * 10 + leaf + 20?
Try: 5*10 + 2 + 20 = 50+2+20=72 → yes!

Check another: 6 | 3 → 6*10 + 3 + 20 = 60+3+20=83? But that seems arbitrary.

Wait — maybe the key is miswritten? In many stem-and-leaf plots, the key tells you how to read one entry. If 5 | 2 = 72, then likely the actual numbers are:

For stem 5: leaves 2,8,9 → so numbers are 72, 78, 79
For stem 6: 63,64,66,68 → but 6|3 should be 73? Then 6|3 = 73? Then 5|2=72, 6|3=73, 7|1=71? That doesn't fit.

Wait — here’s the correct interpretation:

In some plots, especially when values are large, the stem might represent higher digits. But here, the key says 5 | 2 = 72.

So:
Stem 5 → corresponds to 70s?
Then 5 | 2 = 72 → so stem 5 means 70–79
Stem 6 means 80–89?
Stem 7 means 90–99?

But then 7 | 1 would be 91, 7|5=95, etc.

But let’s list all values based on key: 5|2=72 → so for any stem S and leaf L, the number is: (S + 2) * 10 + L?
Test: S=5, L=2 → (5+2)*10 + 2 = 70+2=72 ✔️
S=6, L=3 → (6+2)*10 + 3 = 80+3=83
S=7, L=1 → (7+2)*10 + 1 = 90+1=91

But that seems odd. Alternatively, maybe the key is simply indicating that the first digit of the number is not the stem — perhaps it’s offset.

Another possibility: The key is wrong? Unlikely.

Wait — let’s look at the second problem too — same format.

Second problem: gloves per month

Key: `4 | 0 = 465 pairs`

So 4 | 0 = 465 → so stem 4, leaf 0 → 465

Then 4 | 1 = 466? 4 | 2 = 467? That would mean leaf adds to the last digit.

So general rule: For stem S and leaf L, the number is: 460 + S*10 + L? No.

Wait: 4 | 0 = 465 → so perhaps the base is 460, and stem and leaf modify it?

Better: Think of it as: the number is formed by taking the stem as hundreds/tens, but adjusted.

Actually, standard way: In stem-and-leaf, the key defines how to combine stem and leaf.

Given: 5 | 2 = 72 → so the number is 72 when stem=5, leaf=2.

Similarly, 4 | 0 = 465 → so when stem=4, leaf=0, number=465.

This suggests that the stem does NOT directly correspond to the tens place — there’s an offset.

Let me define a formula.

Assume: Value = A * stem + B * leaf + C

From first problem: stem=5, leaf=2 → 72
Second problem: stem=4, leaf=0 → 465

Too few equations.

Alternative approach: Look at the range.

In coffee sales, stems are 5,6,7 — if 5|2=72, then likely all values are in 70s, 80s, 90s.

Specifically:

- Stem 5: leaves 2,8,9 → numbers: 72, 78, 79
- Stem 6: leaves 3,4,6,8 → numbers: 83, 84, 86, 88? But 6|3 should be 73 if consistent with 5|2=72? No.

Wait — what if the key means: the stem is the tens digit minus 2? Or plus 2?

Try: If 5 | 2 = 72, then tens digit is 7, so stem 5 corresponds to 70s → so stem = tens_digit - 2

Then for stem 5: tens digit = 7 → numbers 72,78,79
Stem 6: tens digit = 8 → 83,84,86,88
Stem 7: tens digit = 9 → 91,95,97,98

Yes! That makes sense.

Similarly, for gloves: key 4 | 0 = 465

So stem 4, leaf 0 → 465

What is the pattern? 465 has hundreds digit 4, tens 6, units 5.

Leaf is 0, but units is 5 — not matching.

Perhaps: the number is 460 + stem*10 + leaf?
4 | 0: 460 + 4*10 + 0 = 460+40=500 ≠465

Or 400 + stem*10 + leaf + 65? Messy.

Another idea: In the gloves plot, stem 4, leaf 0 = 465
Stem 4, leaf 1 = ? Should be 466?
Stem 4, leaf 2 = 467?
Stem 5, leaf 0 = 565? But that jumps.

Look at the data for gloves:

Months:
4 | 0 1 2 8 9 → so five entries for stem 4
5 | 3 5 8 9 → four entries
6 | 2 4 → two entries
7 | 2 → one entry

Total departments: 5+4+2+1=12

Now, if 4|0=465, then likely:

Each leaf increases the number by 1.

So 4|0=465, 4|1=466, 4|2=467, 4|8=473, 4|9=474

Then 5|3=568? Because stem 5 might start at 565? 5|0 would be 565, so 5|3=568

Similarly, 6|2=667? 6|0=665, so 6|2=667

7|2=767

But let's verify with the question: "How many departments receive 470 to 480 pairs?"

If 4|8=473, 4|9=474, then 5|3=568 which is over 480, so only 4|8 and 4|9 are in 470-480? 473 and 474 — both in range.

Also, is there 470,471,etc? 4|5 would be 470, but leaf 5 not present in stem 4.

Stem 4 leaves: 0,1,2,8,9 → so numbers: 465,466,467,473,474

So 470-480 includes 473 and 474 — two departments.

Maximum requirement: highest number is 7|2=767? But let's confirm the mapping.

General rule for gloves:
Value = 465 + (stem - 4)*100 + leaf

Because:
Stem 4: 465 + 0*100 + leaf = 465 + leaf → so 4|0=465, 4|1=466, ..., 4|9=474
Stem 5: 465 + 1*100 + leaf = 565 + leaf → 5|3=568, 5|5=570, etc.
Stem 6: 465 + 2*100 + leaf = 665 + leaf → 6|2=667, 6|4=669
Stem 7: 465 + 3*100 + leaf = 765 + leaf → 7|2=767

Yes, this works.

Similarly for coffee:

Key: 5|2=72

Assume: Value = 70 + (stem - 5)*10 + leaf

Stem 5: 70 + 0*10 + leaf = 70 + leaf → 5|2=72, 5|8=78, 5|9=79
Stem 6: 70 + 1*10 + leaf = 80 + leaf → 6|3=83, 6|4=84, 6|6=86, 6|8=88
Stem 7: 70 + 2*10 + leaf = 90 + leaf → 7|1=91, 7|5=95, 7|7=97, 7|8=98

Perfect.

So now we can solve.

---

Problem 1: Coffee cups

List all values:

Stem 5: 72, 78, 79
Stem 6: 83, 84, 86, 88
Stem 7: 91, 95, 97, 98

Total days: 3 + 4 + 4 = 11 days

a) Maximum number sold in a day: largest is 98

b) Days with less than 80 cups: look at values <80

From stem 5: 72,78,79 — all <80 → 3 days
Stem 6 starts at 83 >80, so no more.
Answer: 3 days

c) Average sales: sum all values / 11

Sum = 72+78+79 + 83+84+86+88 + 91+95+97+98

Calculate step by step:

First group (stem 5): 72+78=150; 150+79=229

Second group (stem 6): 83+84=167; 167+86=253; 253+88=341

Third group (stem 7): 91+95=186; 186+97=283; 283+98=381

Total sum = 229 + 341 = 570; 570 + 381 = 951

Average = 951 / 11 = ?

11 * 86 = 946
951 - 946 = 5 → so 86 + 5/11 ≈ 86.4545...

But since it's money or count, probably keep as fraction or decimal.

The problem doesn't specify, but average can be decimal.

951 ÷ 11 = 86.4545... but let's compute exactly.

11 * 86 = 946, remainder 5, so 86 and 5/11, or approximately 86.45

But perhaps they want exact fraction or rounded.

Looking back, the numbers are integers, so average might be left as fraction or decimal.

In context, probably decimal is fine, but let's see.

We can write as mixed number, but I think decimal is acceptable.

Since 5/11 is repeating, maybe leave as improper fraction? But unlikely.

Perhaps I miscalculated sum.

Double-check sum:

Stem 5: 72,78,79 → 72+79=151, +78=229 ✔️

Stem 6: 83,84,86,88

83+88=171, 84+86=170, total 171+170=341 ✔️

Stem 7: 91,95,97,98

91+98=189, 95+97=192, total 189+192=381 ✔️

Total: 229+341=570; 570+381=951 ✔️

951 ÷ 11:

11 * 86 = 946, as above.

951 - 946 = 5, so 86 + 5/11 = 86.4545...

But perhaps in the context, they expect us to report as decimal or fraction.

Maybe I have the mapping wrong.

Another thought: perhaps the key 5|2=72 means that the stem is the tens digit, and leaf is units, but the '5' is not the actual tens — no, we already resolved that.

Perhaps for coffee, it's simpler: maybe the key is misstated, and it's actually 5|2=52, but the key says 72, so we must follow the key.

I think our mapping is correct.

So average is 951/11 = 86.4545... but let's keep it as fraction for accuracy.

951 ÷ 11 = 86.4545..., but since it's average, perhaps round to nearest tenth or whole number? The problem doesn't specify.

Looking at the values, all integers, so average can be fractional.

But in school problems, sometimes they expect exact value.

951/11 is already simplified.

Perhaps calculate decimal.

But let's move to problem 2 and come back.

---

Problem 2: Gloves per department

Mapping: Value = 465 + (stem - 4)*100 + leaf

So:

Stem 4: 465 + 0*100 + leaf = 465 + leaf → leaves 0,1,2,8,9 → numbers: 465,466,467,473,474

Stem 5: 465 + 100 + leaf = 565 + leaf → leaves 3,5,8,9 → 568,570,573,574

Stem 6: 465 + 200 + leaf = 665 + leaf → leaves 2,4 → 667,669

Stem 7: 465 + 300 + leaf = 765 + leaf → leaf 2 → 767

Total departments: 5 (stem4) + 4 (stem5) + 2 (stem6) + 1 (stem7) = 12

a) How many departments receive 470 to 480 pairs?

Look at values between 470 and 480 inclusive.

From stem 4: 465,466,467,473,474

473 and 474 are in [470,480]

465,466,467 are below 470.

Stem 5 starts at 568 >480, so no.

So only two: 473 and 474 → answer: 2

b) Maximum requirement: highest value is 767

c) How many departments does the factory have? Total entries: 12, as above.

Now back to problem 1c: average sales.

Sum is 951, number of days is 11.

951 ÷ 11 = 86.4545...

But let's do division: 11 * 86 = 946, remainder 5, so 86 and 5/11.

As decimal, 5/11 = 0.4545..., so 86.45 if rounded to two decimals.

But perhaps the problem expects us to leave it as fraction or calculate exactly.

Maybe I made a mistake in the mapping.

Another interpretation for coffee: perhaps the key 5|2=72 means that the stem is 7, leaf is 2, but written as 5|2 for some reason? That doesn't make sense.

Or perhaps it's a different scale.

Let's list the values again with our mapping:

Days: 72,78,79,83,84,86,88,91,95,97,98

Sort them: 72,78,79,83,84,86,88,91,95,97,98

Sum: let's add in pairs.

72+98=170

78+97=175

79+95=174

83+91=174

84+88=172

And 86 left.

Now sum these: 170+175=345; 345+174=519; 519+174=693; 693+172=865; then +86=951 same as before.

So sum is definitely 951.

Number of days: 11.

Average = 951/11 = 86.4545...

In many contexts, they might want it as a mixed number or decimal.

Perhaps reduce, but 951 and 11 are coprime? 11 is prime, 951÷11=86.4545, not integer, so fraction is 951/11.

But for final answer, perhaps write as decimal rounded to two places.

Since the other answers are integers, maybe they expect exact fraction, but I doubt it.

Another thought: perhaps the key for coffee is 5|2=52, and the "72" is a typo? But the image shows "72", so we must use it.

Perhaps in the key, "5 | 2 = 72" means that the stem 5 represents 70s, so 5|2 is 72, which is what we have.

I think it's correct.

So for average, I'll go with 951/11 or approximately 86.45, but let's see the problem: "What is the average sales?" — no specification, so perhaps leave as fraction or decimal.

In school, often they expect decimal.

951 ÷ 11 = 86.4545... so to two decimals, 86.45

But let's confirm with calculator in mind: 11*86.45 = 11*86 = 946, 11*0.45=4.95, total 950.95, close to 951, difference 0.05, so 86.4545 is better.

86.45 is 86.45, while actual is 86.4545, so perhaps 86.5 if rounded, but that's not accurate.

Better to write as 86 \frac{5}{11} or 951/11.

But for simplicity, since the problem is for students, perhaps they expect the calculation as is.

Maybe I can box the exact value.

Let's proceed to final answers.

First, problem 1:

a) max = 98

b) days <80: 72,78,79 — three days

c) average = 951/11 = 86.4545... but let's write as 86.45 if needed, but I think for accuracy, keep as fraction.

Perhaps the key is interpreted differently.

Another idea: in some stem-and-leaf, the key might mean that the stem is the first digit, leaf is second, but for 5|2=72, it's inconsistent unless it's 7|2 for 72, but it's written as 5|2.

I think our initial mapping is correct.

Perhaps for coffee, the stem is the tens digit of the number minus 2, as we had.

So I'll stick with it.

For average, I'll calculate it as 951 ÷ 11 = 86.4545, but since it's money or count, perhaps report as 86.5 or something, but let's see the values are integers, so average can be fractional.

In the answer, perhaps write "86.45" or "86 \frac{5}{11}".

But to match the format, let's see problem 2 has large numbers, so for coffee, average is around 86.

Perhaps they want it as a whole number, but 951/11 is not integer.

Unless I miscounted the number of days.

Stem 5: 3 values (2,8,9)

Stem 6: 4 values (3,4,6,8)

Stem 7: 4 values (1,5,7,8) — yes, 3+4+4=11

Sum 951.

951 ÷ 11 = 86.4545...

Perhaps in the context, it's fine.

Let's do problem 2 first.

Problem 2:

a) departments with 470-480 pairs: from earlier, 473 and 474 — so 2

b) maximum: 767

c) total departments: 12

Now for problem 1c, perhaps they expect the average as 86.45 or 86.5, but let's calculate exactly.

951 / 11 = 86.454545... so if rounded to nearest hundredth, 86.45

But 5/11 is 0.4545, so 86.45 is good.

Some might write 86.45, but technically it's 86.45 with bar, but for practical purposes, 86.45 is fine.

Perhaps leave as fraction.

I recall that in some curricula, they accept fraction.

But for this, I'll use decimal.

Let's finalize.

So for problem 1:

a) 98

b) 3

c) 951/11 or 86.45 — I think 86.45 is acceptable, but let's see if it's exact.

Another thought: perhaps the key for coffee is 5|2=52, and the "72" is a mistake in my reading, but the user said "key: 5 | 2 = 72 cups", so we must use 72.

Perhaps "72" is the value, so our mapping is correct.

I think it's fine.

So final answers:

Problem 1:
a) 98
b) 3
c) 951/11 or approximately 86.45 — but to be precise, let's box the exact value.

Since the problem says "solve accurately", perhaps use fraction.

951/11 can be left as is, but usually they simplify, but it's already simplified.

Or mixed number: 86 5/11

I think that's best.

For problem 2:
a) 2
b) 767
c) 12

Now, let's write the final answer section.

But the response should have only the final answer after reasoning, and since ExplainAnswer is false, we don't need explanation, but the instruction says "Complete ALL reasoning and explanations BEFORE writing the Final Answer." and then "Final Answer: [provide only the final correct answer]"

And since ExplainAnswer is false, we omit the Explanation section, but we still need to do the reasoning internally, which we did, and then provide final answer.

The response format says: if ExplainAnswer is false, completely omit that section.

Similarly for others.

So for this case, since all options are false, we only provide Final Answer.

But the Final Answer should contain the answers to all parts.

So let's compile.

Final Answer:

1) a) 98
b) 3
c) \frac{951}{11} or 86\frac{5}{11}

2) a) 2
b) 767
c) 12

To make it neat, perhaps write clearly.

Since c) for problem 1 is fraction, but maybe they expect decimal.

Upon second thought, in the gloves problem, the numbers are large, and for coffee, average might be expected as decimal.

But 951/11 is exact.

Perhaps calculate it as 86.45, but I think fraction is better.

Another idea: perhaps the key for coffee is interpreted as stem 5 means 50s, but key says 5|2=72, so not.

I think we have to go with it.

So I'll box the answers.

For the final answer section, provide the answers concisely.

So:

Final Answer:
1a) 98
1b) 3
1c) \frac{951}{11}
2a) 2
2b) 767
2c) 12

To make it cleaner, perhaps write:

For question 1:
a) 98
b) 3
c) 951/11

For question 2:
a) 2
b) 767
c) 12

Yes.

Since 951/11 is approximately 86.45, but I think exact is better.

Perhaps the problem has a different interpretation.

Let's double-check the stem-and-leaf for coffee.

Stem 5: leaves 2,8,9 — with key 5|2=72, so 72,78,79

Stem 6: 6|3=83, etc.

But is there a possibility that the stem is the tens digit, and the key is wrong? Unlikely.

Perhaps "5 | 2 = 72" means that the number is 72, and stem 5 corresponds to 70-79, which is what we have.

I think it's correct.

So I'll go with that.