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. Number 72 is crossed out.
Carol wanted to see how the data would change if she did not include the outlier in her study. The results are shown in the table with the outlier crossed out.
Find each listed value.
Range =
Median =
Lower quartile and upper quartile =
Interquartile range =
Which value was affected the most?
Carol wanted to see how the data would change if she did not include the outlier in her study. The results are shown in the table with the outlier crossed out.
Find each listed value.
Range =
Median =
Lower quartile and upper quartile =
Interquartile range =
Which value was affected the most?
Answers
GPT-4o mini
To analyze the data while excluding the outlier (72) and calculating the requested statistics, we will first use the remaining values from the "Watch News" column: 35, 45, 26, 32, 46, 38, 39, 40, 26.
### Step 1: Organize the Data
Let's first sort the values in ascending order:
- Sorted Data: 26, 26, 32, 35, 38, 39, 40, 45, 46
### Step 2: Calculate the Statistics
1. **Range**:
- Range = Maximum value - Minimum value
- Range = 46 - 26 = **20**
2. **Median**:
- Since there are 9 values, the median is the middle value (5th value in a sorted list).
- Median = 38
3. **Lower Quartile (Q1) and Upper Quartile (Q3)**:
- **Lower Quartile (Q1)** is the median of the first half of the data.
- First half (values below the median): 26, 26, 32, 35
- Q1 = (26 + 32) / 2 = 29
- **Upper Quartile (Q3)** is the median of the second half of the data.
- Second half (values above the median): 39, 40, 45, 46
- Q3 = (40 + 45) / 2 = 42.5
4. **Interquartile Range (IQR)**:
- IQR = Q3 - Q1
- IQR = 42.5 - 29 = **13.5**
### Summary of Values
1. **Range** = 20
2. **Median** = 38
3. **Lower Quartile (Q1)** = 29
4. **Upper Quartile (Q3)** = 42.5
5. **Interquartile Range (IQR)** = 13.5
### Step 3: Determine Which Value Was Affected the Most
To determine which value was affected the most by removing the outlier (72), we can consider the change in range and IQR.
- **Original values including outlier**: 26, 26, 32, 35, 38, 39, 40, 45, 46, 72
- Original Range: 72 - 26 = 46
- Original IQR (from previous calculations with outlier): still need to calculate.
Including the outlier:
- New Q1: (32 + 35)/2 = 33.5
- New Q3: (40 + 45)/2 = 42.5
- New IQR with outlier (among values 26, 26, 32, 35, 38, 39, 40, 45, 46, 72): Q3 - Q1 = 42.5 - 33.5 = 9.
From this analysis, the IQR was significantly affected by the presence of the outlier.
**Conclusion**: Removing the outlier (72) decreased the range and changed the quartiles, but the value that was most influenced among the statistics is the **Range**, shifting from 46 to 20.
### Step 1: Organize the Data
Let's first sort the values in ascending order:
- Sorted Data: 26, 26, 32, 35, 38, 39, 40, 45, 46
### Step 2: Calculate the Statistics
1. **Range**:
- Range = Maximum value - Minimum value
- Range = 46 - 26 = **20**
2. **Median**:
- Since there are 9 values, the median is the middle value (5th value in a sorted list).
- Median = 38
3. **Lower Quartile (Q1) and Upper Quartile (Q3)**:
- **Lower Quartile (Q1)** is the median of the first half of the data.
- First half (values below the median): 26, 26, 32, 35
- Q1 = (26 + 32) / 2 = 29
- **Upper Quartile (Q3)** is the median of the second half of the data.
- Second half (values above the median): 39, 40, 45, 46
- Q3 = (40 + 45) / 2 = 42.5
4. **Interquartile Range (IQR)**:
- IQR = Q3 - Q1
- IQR = 42.5 - 29 = **13.5**
### Summary of Values
1. **Range** = 20
2. **Median** = 38
3. **Lower Quartile (Q1)** = 29
4. **Upper Quartile (Q3)** = 42.5
5. **Interquartile Range (IQR)** = 13.5
### Step 3: Determine Which Value Was Affected the Most
To determine which value was affected the most by removing the outlier (72), we can consider the change in range and IQR.
- **Original values including outlier**: 26, 26, 32, 35, 38, 39, 40, 45, 46, 72
- Original Range: 72 - 26 = 46
- Original IQR (from previous calculations with outlier): still need to calculate.
Including the outlier:
- New Q1: (32 + 35)/2 = 33.5
- New Q3: (40 + 45)/2 = 42.5
- New IQR with outlier (among values 26, 26, 32, 35, 38, 39, 40, 45, 46, 72): Q3 - Q1 = 42.5 - 33.5 = 9.
From this analysis, the IQR was significantly affected by the presence of the outlier.
**Conclusion**: Removing the outlier (72) decreased the range and changed the quartiles, but the value that was most influenced among the statistics is the **Range**, shifting from 46 to 20.