Histogram displaying the frequency of dog weights in 5-kilogram intervals, based on a dataset of 30 dogs.

Problem Analysis:

The task involves analyzing the weights of 30 dogs, presented in a list, and creating a histogram to visualize the data. The steps include determining the range of the data, choosing an appropriate bin size, calculating frequencies for each bin, and then drawing the histogram.

#### Given Data:
- List of dog weights (in kilograms):
10, 11, 12, 12, 13, 15, 16, 17, 17, 18,
18, 19, 20, 20, 20, 21, 22, 22, 22, 23,
24, 24, 26, 26, 26, 28, 30, 32, 32, 34, 34

#### Key Questions:
1. What are the smallest and largest values in the dataset?
2. What group size or bin size seems reasonable?
3. How do we organize the data into bins and calculate frequencies?
4. How do we draw the histogram?

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Step-by-Step Solution:

#### Step 1: Determine the Range of the Data
- Minimum value: The smallest weight in the dataset is \(10\) kg.
- Maximum value: The largest weight in the dataset is \(34\) kg.

Thus, the range of the data is from \(10\) to \(34\) kg.

#### Step 2: Choose a Reasonable Bin Size
- A bin size of \(5\) kg is chosen because it provides a good balance between having too many bins (which would make the histogram cluttered) and too few bins (which would oversimplify the data).
- The boundaries of the bins will be:
\(10\) to less than \(15\),
\(15\) to less than \(20\),
\(20\) to less than \(25\),
\(25\) to less than \(30\),
\(30\) to less than \(35\).

#### Step 3: Organize the Data into Bins and Calculate Frequencies
We count how many dog weights fall into each bin:

1. Bin: 10 to less than 15
- Weights: \(10, 11, 12, 12, 13\)
- Frequency: \(5\)

2. Bin: 15 to less than 20
- Weights: \(15, 16, 17, 17, 18, 18, 19\)
- Frequency: \(7\)

3. Bin: 20 to less than 25
- Weights: \(20, 20, 20, 21, 22, 22, 22, 23, 24, 24\)
- Frequency: \(10\)

4. Bin: 25 to less than 30
- Weights: \(26, 26, 26, 28\)
- Frequency: \(4\)

5. Bin: 30 to less than 35
- Weights: \(30, 32, 32, 34, 34\)
- Frequency: \(5\)

#### Step 4: Create a Frequency Table
The frequency table summarizes the data:

| Weights in kilograms | Frequency |
|----------------------|-----------|
| 10 to less than 15 | 5 |
| 15 to less than 20 | 7 |
| 20 to less than 25 | 10 |
| 25 to less than 30 | 4 |
| 30 to less than 35 | 5 |

#### Step 5: Draw the Histogram
Using the frequency table, we can draw the histogram:
- The x-axis represents the weight ranges (bins).
- The y-axis represents the frequency (number of dogs in each bin).
- Each bar corresponds to a bin, with its height equal to the frequency.

#### Histogram Characteristics:
- The histogram shows the distribution of dog weights.
- The tallest bar is in the bin \(20\) to less than \(25\), indicating that this is the most common weight range.
- The spread of the data is visible, showing that weights are concentrated around the middle ranges but extend up to \(35\) kg.

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Final Answer:

The histogram has been successfully created based on the given data and the chosen bin size. The frequency table and histogram provide a clear visualization of the dog weight distribution.

\[
\boxed{\text{Histogram created with bins of 5 kg, frequencies calculated, and visualized.}}
\]