Question
Diane has the following data:
54 62 m 58 64
If the median is 62, which number could m be?
58 or 67
54 62 m 58 64
If the median is 62, which number could m be?
58 or 67
Answers
GPT-4o mini
To determine the possible value of \( m \) such that the median of the numbers 54, 62, \( m \), 58, and 64 remains 62, let's analyze the dataset.
First, we will sort the data including the variable \( m \) in ascending order. The total number of numbers is 5, and to find the median, we need to locate the middle value, which is the 3rd number in the sorted list.
1. If \( m = 58 \):
- The dataset becomes: 54, 58, 58, 62, 64
- The sorted order is: 54, 58, 58, 62, 64
- The median (3rd number) is 58, which is less than 62. Therefore, \( m \) cannot be 58.
2. If \( m = 67 \):
- The dataset becomes: 54, 62, 58, 64, 67
- The sorted order is: 54, 58, 62, 64, 67
- The median (3rd number) is 62, which satisfies the condition.
Based on the above analysis, the only number that could be \( m \) while keeping the median at 62 is \( 67 \). Thus, \( m \) could be:
**67**
First, we will sort the data including the variable \( m \) in ascending order. The total number of numbers is 5, and to find the median, we need to locate the middle value, which is the 3rd number in the sorted list.
1. If \( m = 58 \):
- The dataset becomes: 54, 58, 58, 62, 64
- The sorted order is: 54, 58, 58, 62, 64
- The median (3rd number) is 58, which is less than 62. Therefore, \( m \) cannot be 58.
2. If \( m = 67 \):
- The dataset becomes: 54, 62, 58, 64, 67
- The sorted order is: 54, 58, 62, 64, 67
- The median (3rd number) is 62, which satisfies the condition.
Based on the above analysis, the only number that could be \( m \) while keeping the median at 62 is \( 67 \). Thus, \( m \) could be:
**67**