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To calculate the sample mean from the histogram, we need to use the data shown in it. Here's the breakdown of the information presented:

The histogram shows the following frequency distribution:
- 0 pets: 4 households
- 1 pet: 7 households
- 2 pets: 6 households
- 3 pets: 14 households
- 4 pets: 14 households

### Step 1: Calculate the Sample Mean
The formula for the sample mean is:

\[
\bar{x} = \frac{\sum (x_i \cdot f_i)}{n}
\]

Where:
- \(x_i\) is the number of pets
- \(f_i\) is the frequency (number of households)
- \(n\) is the total number of households

First, compute the total number of households, \(n\):

\[
n = 4 + 7 + 6 + 14 + 14 = 45
\]

Next, calculate the weighted sum of the dataTo calculate the sample mean from the histogram, we need to use the data shown in it. Here's the breakdown of the information presented:

The histogram shows the following frequency distribution:
- 0 pets: 4 households
- 1 pet: 7 households
- 2 pets: 6 households
- 3 pets: 14 households
- 4 pets: 14 households

### Step 1: Calculate the Sample Mean
The formula for the sample mean is:

\[
\bar{x} = \frac{\sum (x_i \cdot f_i)}{n}
\]

Where:
- \(x_i\) is the number of pets
- \(f_i\) is the frequency (number of households)
- \(n\) is the total number of households

First, compute the total number of households, \(n\):

\[
n = 4 + 7 + 6 + 14 + 14 = 45
\]

Next, calculate the weighted sum of the 

\[
\sum (x_i \cdot f_i) = (0 \cdot 4) + (1 \cdot 7) + (2 \cdot 6) + (3 \cdot 14) + (4 \cdot 14)
\]
\[
= 0 + 7 + 12 + 42 + 56 = 117
\]

Now, the sample mean:

\[
\bar{x} = \frac{117}{45} \approx 2.6
\]

So, the sample mean is approximately **2.6**.

Would you like me to help with the standard deviation calculation next? Feel free to ask any questions.

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### Relative Questions:
1. What is the total number of households represented in the histogram?
2. How is the sample mean affected by extreme values (outliers)?
3. How would you calculate the median of this dataset based on the histogram?
4. Can you explain how to calculate the weighted mean from a frequency distribution?
5. How does the standard deviation give insight into data variability?

### Tip:
Always check if your data is skewed before interpreting the mean, as skewness can affect the mean’s representation of the dataset.

The results of a random sample of the number of pets per household in a region are shown in the histogram. Estimate the sample mean and the sample standard deviation of the data set.

Learn how to estimate the sample mean and standard deviation from a histogram showing the number of pets per household. This problem covers key statistical concepts, including the calculation of the sample mean using a frequency distribution and understanding standard deviation. Suitable for high school students.

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