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 consider the following measures: mean, median, and mode.
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Mean: The mean is calculated by summing the values and dividing by the number of values.
- Sum = 19 + 22 + 19 + 18 + 22 + 19 + 19 + 19 + 21 + 19 + 44 + 55 + 21 + 22 = 319
- Number of values = 14
- Mean = 319 / 14 = 22.79 (approximately)
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Median: The median is the middle value when the dataset is ordered.
- Ordered dataset: {18, 19, 19, 19, 19, 19, 19, 19, 21, 21, 22, 22, 22, 44, 55}
- Since there are 14 values (an even number), the median is the average of the 7th and 8th values.
- The 7th value is 19, and the 8th value is also 19, so the median is (19 + 19) / 2 = 19.
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Mode: The mode is the value that appears most frequently.
- In this dataset, 19 appears 7 times, which is more frequent than any other number.
Now, considering the presence of outliers in this dataset (44 and 55 are significantly higher than the other values), the mean is affected significantly by these outliers, making it a less reliable measure of center in this case.
The mode (19) appears most frequently, and the median (19) is unaffected by the extreme values. Both the mode and median indicate the common or center value of the dataset, while the mean is skewed by the outliers.
In conclusion, the best measure of center for this dataset is the mode (19), as it best represents the most common value without being influenced by the extreme values.