Let's calculate the mean, median, mode, and range of the list of values: 1, 2, 4, 71, 2, 4, 71, 2, 4, 7.
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Mean: \[ \text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} \] \[ \text{Sum} = 1 + 2 + 4 + 71 + 2 + 4 + 71 + 2 + 4 + 7 = 168 \] \[ \text{Number of values} = 10 \] \[ \text{Mean} = \frac{168}{10} = 16.8 \]
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Median: To find the median, we first sort the list: 1, 2, 2, 2, 4, 4, 4, 7, 71, 71 Since there are 10 values (even number), the median will be the average of the 5th and 6th values. \[ \text{Median} = \frac{4 + 4}{2} = 4 \]
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Mode: The mode is the value that appears most frequently. In the sorted list:
- 1 appears 1 time
- 2 appears 3 times
- 4 appears 3 times
- 7 appears 1 time
- 71 appears 2 times
The modes are 2 and 4 (both appear 3 times).
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Range: The range is calculated as: \[ \text{Range} = \text{Maximum value} - \text{Minimum value} \] \[ \text{Maximum} = 71, \quad \text{Minimum} = 1 \] \[ \text{Range} = 71 - 1 = 70 \]
To summarize:
- Mean: 16.8
- Median: 4
- Mode: 2 and 4 (bimodal)
- Range: 70
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