Question
The list shows the age of each volunteer in a group cleaning up litter at a state park.
62 20 18 16 32 60 48 16 48 52 26
A. The median is 32, and the interquartile range is 36.
B. The median is 60, and the interquartile range is 34.
C. The median is 32, and the interquartile range is 34.
D. The median is 60, an the interquartile range is 36.
62 20 18 16 32 60 48 16 48 52 26
A. The median is 32, and the interquartile range is 36.
B. The median is 60, and the interquartile range is 34.
C. The median is 32, and the interquartile range is 34.
D. The median is 60, an the interquartile range is 36.
Answers
GPT-4o mini
To determine the median and the interquartile range (IQR) for the given ages, we first need to sort the data in ascending order.
Here is the sorted list of ages:
```
16, 16, 18, 20, 26, 32, 48, 48, 52, 60, 62
```
### Step 1: Find the Median
The median is the middle value of a sorted list. Since there are 11 values (an odd number), the median is the 6th value in the ordered list.
- Median = 32 (the 6th number in the sorted list)
### Step 2: Find the Quartiles
- **Q1 (1st Quartile)**: The median of the first half of the data (the first 5 numbers: 16, 16, 18, 20, 26).
- Q1 = 18 (the median of these 5 numbers)
- **Q3 (3rd Quartile)**: The median of the second half of the data (the last 5 numbers: 32, 48, 48, 52, 60).
- Q3 = 48 (the median of these 5 numbers)
### Step 3: Calculate the Interquartile Range (IQR)
The IQR is calculated as:
```
IQR = Q3 - Q1
IQR = 48 - 18 = 30
```
### Summary:
- Median = 32
- IQR = 30
Now, comparing with the provided options:
- A. The median is 32, and the interquartile range is 36.
- B. The median is 60, and the interquartile range is 34.
- C. The median is 32, and the interquartile range is 34.
- D. The median is 60, and the interquartile range is 36.
The correct option should state that the median is 32 and the IQR is 30, which is not listed in the choices provided. However, if we only consider the median, options A and C both state that the median is 32, but neither of them correctly states the IQR as 30. Therefore, there might have been an error in the options provided.
Based on the calculations, the best selection that states the median correctly is **C**. However, please note that the IQR stated in C is incorrect.
Here is the sorted list of ages:
```
16, 16, 18, 20, 26, 32, 48, 48, 52, 60, 62
```
### Step 1: Find the Median
The median is the middle value of a sorted list. Since there are 11 values (an odd number), the median is the 6th value in the ordered list.
- Median = 32 (the 6th number in the sorted list)
### Step 2: Find the Quartiles
- **Q1 (1st Quartile)**: The median of the first half of the data (the first 5 numbers: 16, 16, 18, 20, 26).
- Q1 = 18 (the median of these 5 numbers)
- **Q3 (3rd Quartile)**: The median of the second half of the data (the last 5 numbers: 32, 48, 48, 52, 60).
- Q3 = 48 (the median of these 5 numbers)
### Step 3: Calculate the Interquartile Range (IQR)
The IQR is calculated as:
```
IQR = Q3 - Q1
IQR = 48 - 18 = 30
```
### Summary:
- Median = 32
- IQR = 30
Now, comparing with the provided options:
- A. The median is 32, and the interquartile range is 36.
- B. The median is 60, and the interquartile range is 34.
- C. The median is 32, and the interquartile range is 34.
- D. The median is 60, and the interquartile range is 36.
The correct option should state that the median is 32 and the IQR is 30, which is not listed in the choices provided. However, if we only consider the median, options A and C both state that the median is 32, but neither of them correctly states the IQR as 30. Therefore, there might have been an error in the options provided.
Based on the calculations, the best selection that states the median correctly is **C**. However, please note that the IQR stated in C is incorrect.