Question
A 2-column table with 10 rows. Column 1 is labeled Classes with entries Hall, Benny, Leggo, Talle, Flower, Gomez, Range, Book, Toledo, Rich. Column 2 is labeled Watch News with entries 35, 45, 26, 32, 46, 38, 39, 40, 26, 72.
Carol did a study to look at the number of television viewers who watched nightly news in various classes in her school. The results are shown in the table.
Find each listed value.
Range =
Outlier =
Median =
38
Lower quartile and upper quartile =
Interquartile range =
Carol did a study to look at the number of television viewers who watched nightly news in various classes in her school. The results are shown in the table.
Find each listed value.
Range =
Outlier =
Median =
38
Lower quartile and upper quartile =
Interquartile range =
Answers
GPT-4o mini
To analyze the data from the study conducted by Carol, let's first summarize the information given in the table:
| Classes | Watch News |
|---------|------------|
| Hall | 35 |
| Benny | 45 |
| Leggo | 26 |
| Talle | 32 |
| Flower | 46 |
| Gomez | 38 |
| Range | 39 |
| Book | 40 |
| Toledo | 26 |
| Rich | 72 |
**Step 1: Organize the "Watch News" data.**
First, we need to list out all the values from the "Watch News" column:
- 35, 45, 26, 32, 46, 38, 39, 40, 26, 72
**Step 2: Sort the data.**
Sorting these values in ascending order, we get:
- 26, 26, 32, 35, 38, 39, 40, 45, 46, 72
**Step 3: Calculate each listed value.**
1. **Range**:
The range is calculated as the difference between the maximum and minimum values.
- Maximum = 72
- Minimum = 26
\[
\text{Range} = 72 - 26 = 46
\]
2. **Outlier**:
To find outliers, we can use the IQR (Interquartile Range) method.
- First, find the median (Q2), lower quartile (Q1), and upper quartile (Q3).
Median (Q2):
- The median is the average of the 5th and 6th values in the sorted list.
\[
\text{Median} = \frac{38 + 39}{2} = 38.5
\]
Lower Quartile (Q1):
- The lower quartile is the median of the first half of the data (26, 26, 32, 35, 38).
\[
Q1 = 32
\]
Upper Quartile (Q3):
- The upper quartile is the median of the second half of the data (39, 40, 45, 46, 72).
\[
Q3 = 45
\]
IQR = Q3 - Q1:
\[
\text{IQR} = 45 - 32 = 13
\]
Outliers are typically defined as values below \( Q1 - 1.5 \times \text{IQR} \) or above \( Q3 + 1.5 \times \text{IQR} \).
\[
Q1 - 1.5 \times \text{IQR} = 32 - 19.5 = 12.5
\]
\[
Q3 + 1.5 \times \text{IQR} = 45 + 19.5 = 64.5
\]
The values below 12.5 or above 64.5 are considered outliers.
In our case, 72 is an outlier. So, we can summarize:
- **Outlier**: 72
3. **Median**:
Already calculated as:
- **Median**: 38.5
4. **Lower Quartile and Upper Quartile**:
We've calculated these as:
- **Lower Quartile (Q1)**: 32
- **Upper Quartile (Q3)**: 45
5. **Interquartile Range (IQR)**:
Already calculated as:
- **Interquartile Range**: 13
**Final Results:**
- Range = 46
- Outlier = 72
- Median = 38.5
- Lower quartile = 32, Upper quartile = 45
- Interquartile Range = 13
| Classes | Watch News |
|---------|------------|
| Hall | 35 |
| Benny | 45 |
| Leggo | 26 |
| Talle | 32 |
| Flower | 46 |
| Gomez | 38 |
| Range | 39 |
| Book | 40 |
| Toledo | 26 |
| Rich | 72 |
**Step 1: Organize the "Watch News" data.**
First, we need to list out all the values from the "Watch News" column:
- 35, 45, 26, 32, 46, 38, 39, 40, 26, 72
**Step 2: Sort the data.**
Sorting these values in ascending order, we get:
- 26, 26, 32, 35, 38, 39, 40, 45, 46, 72
**Step 3: Calculate each listed value.**
1. **Range**:
The range is calculated as the difference between the maximum and minimum values.
- Maximum = 72
- Minimum = 26
\[
\text{Range} = 72 - 26 = 46
\]
2. **Outlier**:
To find outliers, we can use the IQR (Interquartile Range) method.
- First, find the median (Q2), lower quartile (Q1), and upper quartile (Q3).
Median (Q2):
- The median is the average of the 5th and 6th values in the sorted list.
\[
\text{Median} = \frac{38 + 39}{2} = 38.5
\]
Lower Quartile (Q1):
- The lower quartile is the median of the first half of the data (26, 26, 32, 35, 38).
\[
Q1 = 32
\]
Upper Quartile (Q3):
- The upper quartile is the median of the second half of the data (39, 40, 45, 46, 72).
\[
Q3 = 45
\]
IQR = Q3 - Q1:
\[
\text{IQR} = 45 - 32 = 13
\]
Outliers are typically defined as values below \( Q1 - 1.5 \times \text{IQR} \) or above \( Q3 + 1.5 \times \text{IQR} \).
\[
Q1 - 1.5 \times \text{IQR} = 32 - 19.5 = 12.5
\]
\[
Q3 + 1.5 \times \text{IQR} = 45 + 19.5 = 64.5
\]
The values below 12.5 or above 64.5 are considered outliers.
In our case, 72 is an outlier. So, we can summarize:
- **Outlier**: 72
3. **Median**:
Already calculated as:
- **Median**: 38.5
4. **Lower Quartile and Upper Quartile**:
We've calculated these as:
- **Lower Quartile (Q1)**: 32
- **Upper Quartile (Q3)**: 45
5. **Interquartile Range (IQR)**:
Already calculated as:
- **Interquartile Range**: 13
**Final Results:**
- Range = 46
- Outlier = 72
- Median = 38.5
- Lower quartile = 32, Upper quartile = 45
- Interquartile Range = 13