To determine the best value that represents all the measures of center (mean, median, and mode) for the data set, we first need to calculate each of these measures.
Data set: 48, 12, 11, 45, 48, 48, 43, 32
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Mean (Average): \[ \text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} = \frac{48 + 12 + 11 + 45 + 48 + 48 + 43 + 32}{8} = \frac{239}{8} = 29.875 \]
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Median:
- First, we arrange the data in ascending order: 11, 12, 32, 43, 45, 48, 48, 48
- Since there are 8 values, the median is the average of the 4th and 5th values. \[ \text{Median} = \frac{43 + 45}{2} = \frac{88}{2} = 44 \]
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Mode:
- The mode is the value that appears most frequently in the data set. Here, 48 appears three times, which is more than any other number. \[ \text{Mode} = 48 \]
Now we summarize our findings:
- Mean: 29.875
- Median: 44
- Mode: 48
Conclusion: The best value that represents all the measures of center is 48, as it is the mode and the value representing the highest frequency in the data set.