To find the mean, median, and mode of the data set: 45, 52, 17, 63, 57, 42, 54, 58, we perform the following calculations:
1. Mean: The mean is calculated by adding all the numbers together and dividing by the total count of numbers.
\[ \text{Mean} = \frac{45 + 52 + 17 + 63 + 57 + 42 + 54 + 58}{8} \]
Calculating the sum:
\[ 45 + 52 + 17 + 63 + 57 + 42 + 54 + 58 = 45 + 52 + 17 + 63 + 57 + 42 + 54 + 58 = 388 \]
Now, divide by the count of numbers (8):
\[ \text{Mean} = \frac{388}{8} = 48.5 \]
2. Median: To find the median, we first need to sort the data in ascending order:
\[ 17, 42, 45, 52, 54, 57, 58, 63 \]
Since there are 8 numbers (an even count), the median will be the average of the two middle numbers (4th and 5th):
\[ \text{Median} = \frac{52 + 54}{2} = \frac{106}{2} = 53 \]
3. Mode: The mode is the number that appears most frequently in the data set. In this case, all numbers are unique, so there is no mode.
Now summarizing the results:
- Mean: 48.5
- Median: 53
- Mode: None
Based on the above calculations, the correct response is: The mean is 48.5, the median is 53, and there is no mode.