Activity 2: Investigating Outliers This data set is the average amount of money, in thousands of dollars, per year, spent on each person in the country (per capita spending) for health care in 43 countries in 2019. 



1.154       1.213     1.337     1.907     1.973     1.996     2.008     2.159     2.222     2.230     2.354     2.384     2.579       2.638     2.790     2.932     3.224     3.379     3.384     3.428     3.616     3.649     4.204     4.224     4.262       4.578     4.653     4.811     4.823     5.187     5.276     5.376      5.418     5.428     5.558     5.568     5.765       5.782     5.851     6.646     6.647     7.732     11.072



To investigate the outliers in this dataset of per capita healthcare spending in 43 countries in 2019, we need to identify data points that significantly deviate from the rest. Outliers can be detected using statistical methods such as:

1. **Boxplot and Interquartile Range (IQR) Method**: This method identifies outliers as points that are more than 1.5 times the IQR above the third quartile (Q3) or below the first quartile (Q1).
  
2. **Z-score Method**: Data points with Z-scores greater than 3 or less than -3 are often considered outliers. A Z-score indicates how many standard deviations an element is from the mean.

Let's begin by calculating the key statistics: the minimum, first quartile (Q1), median, third quartile (Q3), maximum, mean, standard deviation, and then use these to identify any outliers using the IQR method. 

### Step-by-Step Analysis

1. **Sort the Data**: This will help in calculating the quartiles.
2. **Calculate Quartiles and IQR**:
   - First Quartile (Q1): 25th percentile
   - Third Quartile (Q3): 75th percentile
   - IQR = Q3 - Q1
3. **Identify Outliers**:
   - Lower Bound = Q1 - 1.5 * IQR
   - Upper Bound = Q3 + 1.5 * IQR
   - Any data points outside these bounds are considered outliers.

Let's perform these calculations.Here are the key statistics and findings from the dataset of per capita healthcare spending:

- **First Quartile (Q1)**: 2.369
- **Third Quartile (Q3)**: 5.397
- **Interquartile Range (IQR)**: 3.028
- **Lower Bound for Outliers**: -2.173 (no values below this bound in the dataset)
- **Upper Bound for Outliers**: 9.939

**Outliers Identified**:
- The only outlier in this dataset is **11.072**, which is above the upper bound of 9.939.

**Additional Statistics**:
- **Mean**: 4.033
- **Median**: 3.649
- **Standard Deviation**: 1.968
- **Minimum Value**: 1.154
- **Maximum Value**: 11.072

The outlier is notably higher than the rest of the values, suggesting that one country significantly exceeds the others in per capita healthcare spending.

### Do you want details or have any questions?

Here are 5 related questions to expand on the topic:
1. What country corresponds to the identified outlier value of 11.072?
2. How does the presence of the outlier affect the mean and median of the dataset?
3. Can we analyze how the outlier affects the overall distribution of the data?
4. What methods can be used to mitigate the impact of outliers in statistical analysis?
5. How does healthcare spending compare between countries near the median versus the outlier?

**Tip**: Outliers can significantly skew the results of statistical analysis. Always check for them and consider their impact on measures like the mean and standard deviation.

Activity 2: Investigating Outliers. This data set is the average amount of money, in thousands of dollars, per year, spent on each person in the country (per capita spending) for health care in 43 countries in 2019.

Analyze the 2019 healthcare spending data of 43 countries using statistical techniques like IQR and Z-scores to identify outliers. Learn how quartiles and interquartile ranges help detect outliers, with key statistical measures such as the mean, median, and standard deviation. Suitable for Grades 10-12.

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