**b.** Use *z*-scores to determine if there are any outliers in the house value data. **(Round your answers to 2 decimal places. Negative values should be indicated by a minus sign.)**

To determine if there are any outliers in a dataset using *z*-scores, we first need to calculate the *z*-score for each data point. The *z*-score measures how many standard deviations a data point is from the mean of the dataset.

### Steps to Calculate Z-Scores and Identify Outliers:

1. **Calculate the Mean (\(\mu\)) and Standard Deviation (\(\sigma\)) of the Dataset:**
   \[
   \text{Mean } (\mu) = \frac{\sum X}{N}
   \]
   \[
   \text{Standard Deviation } (\sigma) = \sqrt{\frac{\sum (X - \mu)^2}{N}}
   \]

2. **Calculate the *z*-score for Each Data Point:**
   The *z*-score formula for a value \(X_i\) is:
   \[
   z_i = \frac{X_i - \mu}{\sigma}
   \]

3. **Identify Outliers:**
   Typically, a data point is considered an outlier if its *z*-score is less than -3 or greater than 3. Some stricter interpretations may use -2.5 and 2.5 as cutoffs.

### Example Calculation:

To proceed with these steps, I need the actual data points of the house values to compute the mean, standard deviation, and *z*-scores. If you provide the dataset, I can perform these calculations for you.

Please provide the house value data, or let me know if you need help with an example dataset. 

Would you like to continue with more details or have any questions?

### Related Questions:

1. What is the significance of the *z*-score in statistics?
2. How do you interpret *z*-scores in a real-world context?
3. What is the relationship between standard deviation and *z*-scores?
4. How do different thresholds for *z*-scores affect the identification of outliers?
5. What are other methods to detect outliers in a dataset besides *z*-scores?

**Tip:** When working with real-world data, always visualize the data distribution (e.g., with a histogram or box plot) to better understand potential outliers.

Use z-scores to determine if there are any outliers in the house value data. (Round your answers to 2 decimal places. Negative values should be indicated by a minus sign.)

Learn how to use z-scores to identify outliers in house value data. This example covers calculating the mean, standard deviation, and z-scores, with detailed steps and key formulas. Suitable for students in Grades 10-12.

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