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Bot GPT 4-o mini To determine the "usual" values in the dataset, we can use the interquartile range (IQR) method. The typical approach is to find the first (Q1) and third quartiles (Q3), and then calculate the IQR as follows:
1. **Sort the Data**: Arrange the data in ascending order.
2. **Calculate Q1 and Q3**:
- Q1 is the median of the first half of the data.
- Q3 is the median of the second half of the data.
3. **Calculate IQR**: IQR = Q3 - Q1
4. **Determine Limits**:
- Lower limit = Q1 - 1.5 * IQR
- Upper limit = Q3 + 1.5 * IQR
5. **Count Outliers**: Any values below the lower limit or above the upper limit are considered outliers.
### Step 1: Sort the Data
Sorted list of ages:
20, 20, 21, 22, 23, 24, 25, 25, 26, 27, 27, 27, 28, 28, 28, 28, 29, 29, 29, 29, 30, 31, 31, 31, 31, 32, 33, 33, 33, 33, 34, 34, 34, 35, 35, 35, 35, 36, 36, 36, 36, 36, 37, 37, 37, 38, 38, 38, 38, 39, 39, 40, 41, 42, 62
### Step 2: Calculate Q1 and Q3
- Number of data points: 54
- Q1 is the median of the first 27 values.
- Q3 is the median of the last 27 values.
**Q1 Calculation:**
The first 27 values are from index 0 to 26 (20 to 34 in the sorted list):
(25 + 26) / 2 = 25.5
**Q3 Calculation:**
The last 27 values are from index 27 to 53 (33 to 62 in the sorted list):
(38 + 39) / 2 = 38.5
### Step 3: Calculate IQR
IQR = Q3 - Q1 = 38.5 - 25.5 = 13
### Step 4: Determine Limits
- Lower limit = Q1 - 1.5 * IQR = 25.5 - 1.5 * 13 = 25.5 - 19.5 = 6
- Upper limit = Q3 + 1.5 * IQR = 38.5 + 1.5 * 13 = 38.5 + 19.5 = 58
### Step 5: Count Outliers
Outliers are values less than 6 or greater than 58:
- The values in the dataset are: 20, 20, 21, 22, 23, 24, 25, 25, 26, 27, 27, 27, 28, 28, 28, 28, 29, 29, 29, 29, 30, 31, 31, 31, 31, 32, 33, 33, 33, 33, 34, 34, 34, 35, 35, 35, 35, 36, 36, 36, 36, 36, 37, 37, 37, 38, 38, 38, 38, 39, 39, 40, 41, 42, 62
- Only one value is greater than the upper limit (58): 62.
### Conclusion
- **Usual values** fall between **6 and 58**.
- **Number of outliers** = 1 (the value 62).