Worksheet for creating a back-to-back stem-and-leaf plot with dog weights and related questions.

Let’s solve this step by step.

We are given weights (in pounds) of dogs at a pet adoption center, separated by gender:

Female dogs:
38, 42, 75, 41, 65, 55, 70, 72, 39

Male dogs:
60, 51, 73, 40, 65, 55, 65, 68, 48

---

Step 1: Make a back-to-back stem-and-leaf plot

In a back-to-back stem-and-leaf plot:
- The “stem” is the tens digit.
- The “leaves” are the ones digits.
- Female leaves go on the left, male leaves on the right.
- We list stems from smallest to largest.

First, let’s sort each group:

Female sorted:
38, 39, 41, 42, 55, 65, 70, 72, 75

Male sorted:
40, 48, 51, 55, 60, 65, 65, 68, 73

Now build the plot:

Stems will be: 3, 4, 5, 6, 7

For stem 3:
Female: 8, 9 → write as `9 8 | 3` (left side, usually written in ascending order away from stem? Wait — convention varies. Usually, for back-to-back, female leaves are written in reverse order so they read correctly when viewed from left. But many textbooks just list them in order with female on left and male on right, both increasing outward.)

Actually, standard practice for back-to-back stem-and-leaf:

- Left side (female): leaves increase from right to left (so you read them leftward from the stem)
- Right side (male): leaves increase from left to right

But since the problem doesn’t specify direction, and to keep it simple for students, we’ll do:

Female leaves listed in ascending order *away* from the stem on the left, male on the right also ascending away.

Wait — actually, most common way:

Example:

Stem | Female Leaves | Male Leaves
But no — back-to-back means:

Female Leaves | Stem | Male Leaves

And female leaves are written in reverse order so that when you look at the whole row, the numbers make sense.

Let me clarify with an example:

If female has 38, 39 → under stem 3, female leaves should be written as “9 8” so that reading left to right across the page, it goes 38, 39? No — actually, if you write:

Female | Stem | Male
9 8 | 3 |

That would mean 38 and 39 — because you read the leaf with the stem: 3|8 = 38, 3|9=39. But if you write “9 8” on the left, then reading from left to right, it's 39, 38 — which is descending. So to have ascending order on both sides, we write female leaves in reverse order.

Standard method:

To show data in ascending order overall, for the left side (female), we write the leaves in descending order, so that when you scan down the column, the values increase.

Actually, let’s check a reliable source mentally: In back-to-back plots, the left-side leaves are typically written in reverse order (largest to smallest) so that the entire dataset appears ordered when read top to bottom.

But for simplicity in middle school math, sometimes they just list both sides in ascending order outward.

Given the ambiguity, I’ll follow the most common textbook approach:

→ For each stem, list female leaves in ascending order from right to left (i.e., write them backwards), and male leaves in ascending order left to right.

So for stem 3:

Female: 38, 39 → write as “9 8” on left
Male: none → blank

Stem 4:

Female: 41, 42 → write as “2 1”
Male: 40, 48 → write as “0 8”

Stem 5:

Female: 55 → “5”
Male: 51, 55 → “1 5”

Stem 6:

Female: 65 → “5”
Male: 60, 65, 65, 68 → “0 5 5 8”

Stem 7:

Female: 70, 72, 75 → “5 2 0”
Male: 73 → “3”

Also need key: e.g., 3 | 8 = 38 lb

But note: in back-to-back, the key might say something like:
Key: 3 | 8 = 38 lb (female), 3 | 0 = 30 lb (male) — but since male has no 30s, maybe just define one.

Actually, better key:
Key: Left leaf | stem | right leaf → e.g., 8 | 3 | 0 means 38 lb (female) and 30 lb (male). But since male doesn't have 30, perhaps just use existing.

Alternatively, simpler: Key: 3 | 8 = 38 lb (female), 4 | 0 = 40 lb (male)

But to avoid confusion, let’s define:

Key: A leaf of 8 on the left of stem 3 represents 38 lb (female dog); a leaf of 0 on the right of stem 4 represents 40 lb (male dog).

But for student level, maybe just:

Key: 3 | 8 = 38 lb (female), 4 | 0 = 40 lb (male)

Okay, now construct the plot:

```
Female Stem Male
9 8 3
2 1 4 0 8
5 5 1 5
5 6 0 5 5 8
5 2 0 7 3
```

Key: 3 | 8 = 38 lb (female), 4 | 0 = 40 lb (male)

(Note: Some teachers prefer female leaves written in forward order on left, but then the visual ordering isn't monotonic. Since the problem says "make a back-to-back stem-and-leaf plot", and doesn't specify direction, either is acceptable as long as consistent. But to match typical expectations, I'll go with the above.)

Actually, let me double-check with actual values.

Alternative simpler version (both sides ascending outward):

Some curricula teach:

Female leaves listed in ascending order on the left (so 38,39 becomes 8,9 on left), male on right 0,8 etc.

Then the plot looks like:

```
Female Stem Male
8 9 3
1 2 4 0 8
5 5 1 5
5 6 0 5 5 8
0 2 5 7 3
```

This is also valid and perhaps easier for beginners.

I think for this grade level, this second version is more intuitive.

Let me confirm total counts:

Female: 9 dogs → 38,39,41,42,55,65,70,72,75 → yes

Male: 9 dogs → 40,48,51,55,60,65,65,68,73 → yes

In the plot above:

Stem 3: F:8,9 → 38,39; M: none → correct

Stem 4: F:1,2 → 41,42; M:0,8 → 40,48 → correct

Stem 5: F:5 → 55; M:1,5 → 51,55 → correct

Stem 6: F:5 → 65; M:0,5,5,8 → 60,65,65,68 → correct

Stem 7: F:0,2,5 → 70,72,75; M:3 → 73 → correct

Perfect.

So final plot:

```
Female Stem Male
8 9 3
1 2 4 0 8
5 5 1 5
5 6 0 5 5 8
0 2 5 7 3
```

Key: 3 | 8 = 38 lb (female), 4 | 0 = 40 lb (male)

(You could also write Key: Leaf represents units digit, stem represents tens digit.)

---

Now answer the questions:

1) What is the weight of the heaviest male dog?

Look at male dogs: 40,48,51,55,60,65,65,68,73 → heaviest is 73 lb

2) What is the average weight of female dogs?

Female weights: 38,42,75,41,65,55,70,72,39

Add them up:

38 + 42 = 80
80 + 75 = 155
155 + 41 = 196
196 + 65 = 261
261 + 55 = 316
316 + 70 = 386
386 + 72 = 458
458 + 39 = 497

Total = 497 lb

Number of female dogs = 9

Average = 497 ÷ 9

Calculate: 9 × 55 = 495 → 497 - 495 = 2 → so 55 + 2/9 ≈ 55.222...

But let's do exact division:

497 ÷ 9 = 55.222... → or as fraction 497/9

But probably expect decimal rounded or exact?

Since weights are whole numbers, maybe leave as mixed number or decimal.

497 9 = 55 R 2 → so 55 and 2/9 lb, or approximately 55.2 lb

But let's check addition again to be sure:

List: 38,39,41,42,55,65,70,72,75

Group: (38+39)=77; (41+42)=83; 55; 65; 70; 72; 75

Better:

38 + 39 = 77
41 + 42 = 83
55
65
70
72
75

Now add: 77 + 83 = 160
160 + 55 = 215
215 + 65 = 280
280 + 70 = 350
350 + 72 = 422
422 + 75 = 497 → same as before.

Yes, 497 ÷ 9 = 55.222... → so 55.2 lb if rounding to tenths, or 55 2/9 lb

But in context, probably accept 55.2 or exact fraction. However, looking at the data, all integers, so maybe they want exact value.

But question says "average weight", so decimal is fine.

I'll compute precisely: 497 ÷ 9 = 55.222... → so 55.2 lb (rounded to nearest tenth)

But let's see if it divides evenly? No.

Perhaps leave as 497/9, but unlikely.

Another thought: did I miscount number of females? Original list: Female: 38,42,75,41,65,55,70,72,39 → that's 9 numbers. Yes.

So average = 497 / 9 ≈ 55.222 → I'll report as 55.2 lb for practical purposes.

But to be precise, let's keep it as fraction for now.

3) How many dogs weigh between 30 to 50 pounds?

"Between 30 to 50" — does this include 30 and 50? Typically in such contexts, it means ≥30 and ≤50, or sometimes >30 and <50. Need to interpret.

Looking at data:

Weights from 30 to 50 inclusive:

Female: 38,39,41,42 → all between 30 and 50? 38,39,41,42 are all >30 and <50? 42<50, yes. Is 50 included? There is no 50, but 42 is less than 50.

What about 50 itself? Not present.

Also, 30? Not present.

So dogs with weight ≥30 and ≤50:

Female: 38,39,41,42 → 4 dogs

Male: 40,48 → 2 dogs (since 40 and 48 are between 30 and 50)

Is 50 included? If "between 30 to 50" includes 50, but there is no 50, so same.

What about 51? That's over 50.

So total: 4 (female) + 2 (male) = 6 dogs

But let's list all weights between 30 and 50 inclusive:

From combined list:

Female: 38,39,41,42 → all in [30,50]

Male: 40,48 → in [30,50]

Next is 51, which is over 50.

So yes, 6 dogs.

But is 30 included? Minimum is 38, so no issue.

Answer: 6

4) What is the least weight among the dogs?

Look at all weights:

Female min: 38

Male min: 40

Overall min: 38 lb

5) How many dogs weigh 65 pounds?

Check:

Female: 65 → one

Male: 65,65 → two

Total: 1 + 2 = 3 dogs

Confirm:

Female list: ...65... → yes, one 65

Male list: 65,65 → yes, two 65s

Total: 3

---

Now, summarize answers:

1) Heaviest male: 73 lb

2) Average female weight: 497 ÷ 9 = 55.222... → I'll write as 55.2 lb (but let's calculate exactly)

497 ÷ 9 = 55.222... so to one decimal place, 55.2 lb

But perhaps they want exact fraction? Unlikely. Or maybe I made mistake.

Another way: sum is 497, divided by 9.

9 * 55 = 495, remainder 2, so 55 and 2/9 lb.

In decimal, 55.222..., so if rounding to nearest tenth, 55.2 lb.

I think for this level, 55.2 is acceptable.

But let's see the other answers are integers, so perhaps they expect fraction? No, average can be decimal.

I'll go with 55.2 lb.

To be safe, I can write 55.2 or 55 2/9, but I think 55.2 is fine.

Upon second thought, let's compute numerically:

497 ÷ 9 = 55.222222... so if the problem expects a boxed answer, probably 55.2 or exact.

But looking at the context, I'll use 55.2

However, let me check if I added wrong.

Female weights: 38,42,75,41,65,55,70,72,39

Add in pairs:

38 + 72 = 110

42 + 70 = 112

75 + 39 = 114

41 + 55 = 96

65 alone

Now: 110 + 112 = 222

222 + 114 = 336

336 + 96 = 432

432 + 65 = 497 → same.

Yes.

So average = 497/9 ≈ 55.222 → I'll report as 55.2 lb

But perhaps the problem allows fraction. Since it's weight, decimal is fine.

I recall that in some systems, they might want it as mixed number, but I think for this, 55.2 is okay.

To match precision, since inputs are integers, output can be decimal.

Final decision: 55.2 lb

But let's see question 3: "between 30 to 50" — I assumed inclusive, and got 6.

Is 50 included? There is no 50, so same.

What about 30? No dog weighs 30, min is 38.

So 6 is correct.

Least weight: 38 lb

Dogs weighing 65 lb: 3

Now, for the stem-and-leaf plot, I need to present it clearly.

In the response, since ExplainAnswer is false, I don't need to explain, but I must provide the final answer after reasoning.

The user said ExplainAnswer: false, so I should not include explanation section.

But I did the reasoning above for myself.

Now, for Final Answer, I need to provide all parts.

The task is to solve the problem, which includes making the plot and answering questions.

But in Final Answer, probably list the answers to the questions, and perhaps describe the plot.

Since it's text-based, I'll write the plot as text.

And then the answers.

So:

Final Answer:

Back-to-back stem-and-leaf plot:

```
Female Stem Male
8 9 3
1 2 4 0 8
5 5 1 5
5 6 0 5 5 8
0 2 5 7 3
```

Key: 3 | 8 = 38 lb (female), 4 | 0 = 40 lb (male)

Answers:

1) 73 lb

2) 55.2 lb (or 497/9 lb)

3) 6

4) 38 lb

5) 3

But for question 2, to be precise, let's calculate 497 ÷ 9 exactly.

497 ÷ 9 = 55.222... so if we round to nearest tenth, it's 55.2

Some might argue to keep as fraction, but I think decimal is fine.

I recall that in the initial data, all are integers, but average can be decimal.

Perhaps the problem expects the exact value.

Another thought: maybe I miscalculated the sum.

List female weights again: 38,42,75,41,65,55,70,72,39

Sort them: 38,39,41,42,55,65,70,72,75

Sum: 38+39=77; 41+42=83; 55; 65; 70; 72; 75

77+83=160; 160+55=215; 215+65=280; 280+70=350; 350+72=422; 422+75=497 — yes.

497 / 9 = 55.222... so I'll use 55.2

For consistency, perhaps write as 55.2

Now for the plot, in some formats, the female leaves are written in reverse order, but as I said, for simplicity, I used ascending outward.

To match standard, let me verify with a quick search in my knowledge.

Upon recall, in many textbooks, for back-to-back, the left side (first group) has leaves in reverse order so that the data is ordered when read top to bottom.

For example, for stem 3, female 38,39 — if you write "9 8" on left, then when you read the row, it's 39,38 which is descending, but if you read down the column, it's not ordered.

Actually, the purpose is to compare distributions, so often both sides are sorted in the same direction relative to the stem.

I found a reference in my mind: typically, for back-to-back stem-and-leaf, the leaves on the left are written in descending order, and on the right in ascending order, so that the smallest values are at the top for both groups.

Let me try that.

For stem 3: female 38,39 — to have smallest at top, but 38<39, so if I write "8 9" on left, then 38 is closer to stem? No.

Standard way: the stem is in the middle, left leaves are for first group, right for second, and within each row, the leaves are sorted so that the data increases as you go down the page.

So for female, to have increasing order down the page, for each stem, the leaves should be sorted in ascending order, but since it's on the left, when you read left to right, it might be decreasing, but the vertical order matters.

Perhaps it's better to have for each stem, the female leaves listed in ascending order from the stem outward, but that would mean for stem 3, "8 9" on left, so 38,39.

Then for stem 4, "1 2" for 41,42, etc.

And for male, "0 8" for 40,48.

Then when you look at the plot, for female, as you go down, the values increase: stem 3: 38,39; stem 4:41,42; etc.

Similarly for male.

So the plot I had earlier is fine.

I think it's acceptable.

So I'll stick with:

```
Female Stem Male
8 9 3
1 2 4 0 8
5 5 1 5
5 6 0 5 5 8
0 2 5 7 3
```

Key: 3 | 8 = 38 lb (female), 4 | 0 = 40 lb (male)

Now for the answers.

Question 2: average weight of female dogs.

497 / 9 = 55.222...

Perhaps they want it as a mixed number: 55 2/9 lb

Or decimal.

In the context, since other answers are integers, but average can be decimal.

I can calculate it as 55.2 if rounded, but let's see the exact value.

Another idea: perhaps I can leave it as 497/9, but unlikely.

I recall that in some problems, they expect the calculation.

But for this, I'll use 55.2 lb.

To be accurate, let's box 55.2

But let's check if 497 ÷ 9 is exactly 55.222, so for reporting, 55.2 is fine.

Perhaps the problem has a typo, but no.

I think it's correct.

So final answers:

1) 73

2) 55.2

3) 6

4) 38

5) 3

With units where appropriate.

For the plot, since it's part of the answer, I'll include it in Final Answer.

So:

Final Answer:

Back-to-back stem-and-leaf plot:

```
Female Stem Male
8 9 3
1 2 4 0 8
5 5 1 5
5 6 0 5 5 8
0 2 5 7 3
```

Key: 3 | 8 = 38 lb (female), 4 | 0 = 40 lb (male)

1) 73 lb
2) 55.2 lb
3) 6
4) 38 lb
5) 3

But for question 2, to be precise, let's write it as \frac{497}{9} lb or 55.\overline{2} lb, but for student, 55.2 is sufficient.

I think it's fine.

Perhaps calculate it as 55.22, but no.

Another thought: maybe they want the average without rounding, but in the answer space, probably decimal.

I'll go with 55.2

So here is the final answer.