To determine the best measure of center for the dataset {19, 22, 19, 18, 22, 19, 19, 19, 21, 19, 44, 55, 21, 22}, we can calculate the mean, median, and mode.
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Mean: Calculate the average of the numbers. \[ \text{Mean} = \frac{19 + 22 + 19 + 18 + 22 + 19 + 19 + 19 + 21 + 19 + 44 + 55 + 21 + 22}{14} = \frac{ 19 + 22 + 19 + 18 + 22 + 19 + 19 + 19 + 21 + 19 + 44 + 55 + 21 + 22 }{14} = \frac{ 378}{14} \approx 27 \]
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Median: This is the middle value when the data is sorted. The sorted dataset is: {18, 19, 19, 19, 19, 19, 19, 21, 21, 22, 22, 22, 44, 55}. Since there are 14 values (an even number), the median will be the average of the 7th and 8th values: \[ \text{Median} = \frac{19 + 21}{2} = 20 \]
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Mode: The mode is the value that appears most often. In this dataset, the number 19 appears the most frequently (6 times), followed by 22 (3 times).
Given these measures:
- Mean is approximately 27,
- Median is 20,
- Mode is 19.
Since the dataset contains some significantly high outliers (44 and 55), the mean could be skewed, making it less representative of the center. The mode, 19, represents the most common value in the dataset and is a strong candidate for the best measure of center here.
Therefore, the best measure of center for this dataset is:
Mode.