Question
Use the data set to determine which statements are correct. Check the four that apply.
23, 45, 39, 57, 31, 53, 28, 50, 42, 36
The median is 41.
The upper quartile is 50.
The lower quartile is 36.
The lower quartile is 31.
The median is 40.5.
The upper quartile is 53.
The interquartile range is 19.
23, 45, 39, 57, 31, 53, 28, 50, 42, 36
The median is 41.
The upper quartile is 50.
The lower quartile is 36.
The lower quartile is 31.
The median is 40.5.
The upper quartile is 53.
The interquartile range is 19.
Answers
GPT-4o mini
To evaluate the statements about the dataset, we first need to organize the given numbers and then calculate the median, quartiles, and interquartile range (IQR).
### Step 1: Sort the Data
The dataset in ascending order is:
28, 31, 36, 39, 42, 45, 50, 53, 57
### Step 2: Calculate the Median
The median is the middle number in a sorted list. Since there are 10 numbers (even), the median is the average of the 5th and 6th numbers.
- 5th number: 42
- 6th number: 45
- Median = (42 + 45) / 2 = 87 / 2 = 43.5
### Step 3: Calculate Quartiles
- **Lower Quartile (Q1)**: This is the median of the first half of the data. The first half is: 28, 31, 36, 39, which has 5 numbers.
- Q1 = 36 (the median of the first 5 numbers)
- **Upper Quartile (Q3)**: This is the median of the second half of the data. The second half is: 42, 45, 50, 53, 57, which also has 5 numbers.
- Q3 = 50 (the median of the last 5 numbers)
### Step 4: Calculate the Interquartile Range (IQR)
- IQR = Q3 - Q1 = 50 - 36 = 14
### Final Evaluation of Statements
1. **The median is 41.** (Incorrect, it's 43.5)
2. **The upper quartile is 50.** (Correct)
3. **The lower quartile is 36.** (Correct)
4. **The lower quartile is 31.** (Incorrect, it's 36)
5. **The median is 40.5.** (Incorrect, it's 43.5)
6. **The upper quartile is 53.** (Incorrect, it's 50)
7. **The interquartile range is 19.** (Incorrect, it's 14)
### Correct Statements
The four correct statements are:
- The upper quartile is 50.
- The lower quartile is 36.
- The median is 43.5 (which is not among the options but clarifies the discrepancy).
- Interquartile range is 14 (not mentioned in the options either).
From the provided selections, **the correct statements are:**
- The upper quartile is 50.
- The lower quartile is 36.
However, none of the four original options can be checked off as they all are incorrect or disputed based on a medicated analysis. Thus, only the quartile statements are valid based on sorted data analysis, while the median and IQR differ.
If asked to respond to offered options, state two valid options while clarifying and seeking proper validation as needed.
### Step 1: Sort the Data
The dataset in ascending order is:
28, 31, 36, 39, 42, 45, 50, 53, 57
### Step 2: Calculate the Median
The median is the middle number in a sorted list. Since there are 10 numbers (even), the median is the average of the 5th and 6th numbers.
- 5th number: 42
- 6th number: 45
- Median = (42 + 45) / 2 = 87 / 2 = 43.5
### Step 3: Calculate Quartiles
- **Lower Quartile (Q1)**: This is the median of the first half of the data. The first half is: 28, 31, 36, 39, which has 5 numbers.
- Q1 = 36 (the median of the first 5 numbers)
- **Upper Quartile (Q3)**: This is the median of the second half of the data. The second half is: 42, 45, 50, 53, 57, which also has 5 numbers.
- Q3 = 50 (the median of the last 5 numbers)
### Step 4: Calculate the Interquartile Range (IQR)
- IQR = Q3 - Q1 = 50 - 36 = 14
### Final Evaluation of Statements
1. **The median is 41.** (Incorrect, it's 43.5)
2. **The upper quartile is 50.** (Correct)
3. **The lower quartile is 36.** (Correct)
4. **The lower quartile is 31.** (Incorrect, it's 36)
5. **The median is 40.5.** (Incorrect, it's 43.5)
6. **The upper quartile is 53.** (Incorrect, it's 50)
7. **The interquartile range is 19.** (Incorrect, it's 14)
### Correct Statements
The four correct statements are:
- The upper quartile is 50.
- The lower quartile is 36.
- The median is 43.5 (which is not among the options but clarifies the discrepancy).
- Interquartile range is 14 (not mentioned in the options either).
From the provided selections, **the correct statements are:**
- The upper quartile is 50.
- The lower quartile is 36.
However, none of the four original options can be checked off as they all are incorrect or disputed based on a medicated analysis. Thus, only the quartile statements are valid based on sorted data analysis, while the median and IQR differ.
If asked to respond to offered options, state two valid options while clarifying and seeking proper validation as needed.