To find the mean, median, and mode of the data set \( 45, 52, 17, 63, 57, 42, 54, 58 \), let's calculate each step:
-
Mean:
- To find the mean, sum up all the numbers and then divide by the number of values. \[ 45 + 52 + 17 + 63 + 57 + 42 + 54 + 58 = 388 \]
- There are 8 numbers in the set. \[ \text{Mean} = \frac{388}{8} = 48.5 \]
-
Median:
- First, we need to sort the data set in ascending order: \[ 17, 42, 45, 52, 54, 57, 58, 63 \]
- Since there are 8 values (an even number), the median will be the average of the 4th and 5th values: \[ \text{Median} = \frac{52 + 54}{2} = \frac{106}{2} = 53 \]
-
Mode:
- The mode is the value that appears most frequently. In this dataset, all the numbers occur only once.
- Therefore, there is no mode.
Putting it all together:
- Mean = 48.5
- Median = 53
- Mode = None
Thus, the correct answer is: The mean is 48.5, the median is 53, and there is no mode.