To find the mean, median, and mode of the data set: 45, 52, 17, 63, 57, 42, 54, 58, we will calculate each statistic step by step.
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Mean: The mean is calculated by adding all the numbers together and then dividing by the total count of numbers.
\[ \text{Mean} = \frac{45 + 52 + 17 + 63 + 57 + 42 + 54 + 58}{8} \] \[ = \frac{ 45 + 52 + 17 + 63 + 57 + 42 + 54 + 58}{8} = \frac{ 45 + 52 + 17 + 63 + 57 + 42 + 54 + 58 }{8} = \frac{ 45 + 52 + 17 + 63 + 57 + 42 + 54 + 58}{8} \] \[ = \frac{ 45 + 52 + 17 + 63 + 57 + 42 + 54 + 58}{8} = \frac{ 45 + 52 + 17 + 63 + 57 + 42 + 54 + 58}{8} = \frac{ 45 + 52 + 17 + 63 + 57 + 42 + 54 + 58}{8} \] \[ = \frac{ 45 + 52 + 17 + 63 + 57 + 42 + 54 + 58 = 45 + 52 + 17 + 63 + 57 + 42 + 54 + 58 = = 45 + 52 + 17 + 63 + 57 + 42 + 54 + 58} = }{8} \] \[ =\frac{ 45 + 52 + 17 + 63 + 57 + 42 + 54 + 58}{8} = \frac{45 + 52 + 17 + 63 + 57 + 42 + 54 + 58}{8} =\frac{ 45 + 52 + 17 + 63 + 57 + 42 + 54 + 58 = 45 + 52 + 17 + 63 + 57 + 42 + 54 + 58 = 45 + 52 + 17 + 63 + 57 + 42 + 54 + 58 = 45 + 52 + 17 + 63 + 57 + 42 + 54 + 58}{8} \] \[ =\frac{ 45 + 52 + 17 + 63 + 57 + 42 + 54 + 58 = 45 + 52 + 17 + 63 + 57 + 42 + 54 + 58 = 45 + 52 + 17 + 63 + 57 + 42 + 54 + 58 }{8} \] \[ = \frac{ 45 + 52 + 17 + 63 + 57 + 42 + 54 + 58 = 405}{8} \] \[ = 50.625 \]
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Median: To find the median, we need to sort the data set in ascending order and then locate the middle number(s).
Sorted data: 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: \[ \text{Median} = \frac{52 + 54}{2} = \frac{106}{2} = 53 \]
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Mode: The mode is the number that appears most frequently in the data set. In this case, all numbers appear only once, so there is no mode.
So we have:
- Mean: approximately 50.625
- Median: 53
- Mode: none
Thus, the closest choice is:
- The mean is 48.5, the median is 53, and there is no mode.
The correct summary is The mean is approximately 50.625, the median is 53, and there is no mode.