https://file.aiquickdraw.com/mathbot/file/1725981780317vh5b44f5.jpg

Let's go through the questions step by step based on the dot plot shown in the image.

### Part a: Mean Age
The mean age is calculated by adding up all the individual ages of the dogs and dividing by the total number of dogs (which is 29, as stated in the question). In the image, the sum is given as 125 years, and the calculation is already shown:

\[
\frac{125}{29} = 4.31 \text{ (rounded to the nearest tenth)} \approx 4.3 \text{ years}
\]

So, the mean age of the dogs is **4.3 years**.

### Part b: Explanation of the Mean
You can explain the value of the mean like this:
- To find the mean age, I added up all the ages of the dogs shown in the dot plot, which gave a total of 125 years. Then, I divided this total by the number of dogs, 29, which gave me the mean age. After dividing, I rounded the result to the nearest tenth, which was 4.3 years.

### Part c: Median Age
To find the median, the dogs' ages must be listed in order, and then the middle value is selected. Since there are 29 dogs, the middle position will be the 15th value.

Looking at the dot plot, counting from left to right:
- The 15th dog falls at the age of **4 years**.

Thus, the median age is **4 years**.

### Part d: Explanation of the Median
You can explain the value of the median like this:
- To find the median, I listed the ages of the 29 dogs in order from least to greatest. Since there are 29 dogs, I found the 15th age in this ordered list, which is 4 years, so the median age is 4 years.

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Let me know if you'd like more details, and here are some related questions:

1. What does the mean represent in a set of data like this?
2. How would the mean change if a dog aged 0 years was added to the group?
3. Why is the median sometimes a better representation of "central tendency" than the mean?
4. What would happen to the median if more dogs aged 11 years were added?
5. Can there be more than one mode in a set of data, and how would you find it here?

**Tip**: The median is less sensitive to outliers than the mean, making it a better measure in skewed distributions.

What is the mean and median age of dogs at the park?

Learn how to calculate the mean and median age of dogs using a dot plot. This problem covers key concepts like averaging and finding the median in a dataset, suitable for students in Grades 6-8.

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