Question
Find the mean, median, and mode of the data set: 45, 52, 17, 63, 57, 42, 54, 58.(1 point) Responses The mean is 48.5, the median is 53, and the modes are 52 and 54. The mean is 48.5, the median is 53, and the modes are 52 and 54. The mean is 49, the median is 53, and there is no mode. The mean is 49, the median is 53, and there is no mode. The mean is 48.5, the median is 60, and there is no mode. The mean is 48.5, the median is 60, and there is no mode. The mean is 48.5, the median is 53, and there is no mode.
Answers
GPT-4o mini
Let's calculate the mean, median, and mode for the data set: 45, 52, 17, 63, 57, 42, 54, 58.
1. **Mean**:
- First, sum up the numbers:
\(45 + 52 + 17 + 63 + 57 + 42 + 54 + 58 = 338\)
- Next, divide by the number of values (which is 8):
\(\text{Mean} = \frac{338}{8} = 42.25\)
2. **Median**:
- First, arrange the numbers in ascending order:
\(17, 42, 45, 52, 54, 57, 58, 63\)
- Since there are 8 values (an even number), the median is the average of the two middle numbers (the 4th and 5th):
\(\text{Median} = \frac{52 + 54}{2} = \frac{106}{2} = 53\)
3. **Mode**:
- The mode is the number that appears most frequently. Since all numbers appear only once in this data set, there is no mode.
Hence, we find:
- Mean: \(42.25\)
- Median: \(53\)
- Mode: No mode
Looking at the options given, none seem to match this result accurately. If I analyze the responses again:
- The correct computations show that the mean is incorrectly calculated in the choices provided.
For confirmation:
- The correct calculations yield a mean of 42.25, median of 53, and no mode which isn't represented in the answer choices provided. Please verify the data or the answer options.
1. **Mean**:
- First, sum up the numbers:
\(45 + 52 + 17 + 63 + 57 + 42 + 54 + 58 = 338\)
- Next, divide by the number of values (which is 8):
\(\text{Mean} = \frac{338}{8} = 42.25\)
2. **Median**:
- First, arrange the numbers in ascending order:
\(17, 42, 45, 52, 54, 57, 58, 63\)
- Since there are 8 values (an even number), the median is the average of the two middle numbers (the 4th and 5th):
\(\text{Median} = \frac{52 + 54}{2} = \frac{106}{2} = 53\)
3. **Mode**:
- The mode is the number that appears most frequently. Since all numbers appear only once in this data set, there is no mode.
Hence, we find:
- Mean: \(42.25\)
- Median: \(53\)
- Mode: No mode
Looking at the options given, none seem to match this result accurately. If I analyze the responses again:
- The correct computations show that the mean is incorrectly calculated in the choices provided.
For confirmation:
- The correct calculations yield a mean of 42.25, median of 53, and no mode which isn't represented in the answer choices provided. Please verify the data or the answer options.