To analyze the change in the data set after adding the two new dog weights of 25 pounds and 45 pounds, let's first calculate the current statistics of the initial data set.
The initial weights are:
- 16, 34, 44, 20, 50, 19, 30, 54
Step 1: Calculate the initial statistics
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Mean: \[ \text{Mean} = \frac{16 + 34 + 44 + 20 + 50 + 19 + 30 + 54}{8} = \frac{217}{8} \approx 27.125 \]
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Median: First, sort the data: \[ 16, 19, 20, 30, 34, 44, 50, 54 \] The median will be the average of the 4th and 5th numbers. \[ \text{Median} = \frac{30 + 34}{2} = \frac{64}{2} = 32 \]
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Range: \[ \text{Range} = 54 - 16 = 38 \]
Step 2: Add the new weights and recalculate
New weights added:
- 25, 45
New weights list:
- 16, 34, 44, 20, 50, 19, 30, 54, 25, 45
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New Mean: \[ \text{New Mean} = \frac{217 + 25 + 45}{10} = \frac{287}{10} = 28.7 \]
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New Median: Sort the new weights: \[ 16, 19, 20, 25, 30, 34, 44, 45, 50, 54 \] The median will be the average of the 5th and 6th numbers (30 and 34). \[ \text{New Median} = \frac{30 + 34}{2} = \frac{64}{2} = 32 \]
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New Range: \[ \text{New Range} = 54 - 16 = 38 \quad (\text{No change in range}) \]
Summary of Changes:
- The mean increased from approximately 27.125 to 28.7, indicating that the average weight increased.
- The median remained the same at 32, indicating that the central tendency of the data has not changed.
- The range remained the same at 38, indicating the spread of the weights has not changed.
Conclusion: The addition of the two new dogs resulted in an increase in the mean weight of the dogs in the kennel, while the median and range remained unchanged.