To determine the best measure of center for the given dataset {19, 22, 19, 18, 22, 19, 19, 19, 21, 19, 44, 55, 21, 22}, we can consider the three common measures: mean, median, and mode.
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Mean:
- To calculate the mean, sum all the numbers and divide by the total count.
- Mean = (19 + 22 + 19 + 18 + 22 + 19 + 19 + 19 + 21 + 19 + 44 + 55 + 21 + 22) / 14
- Mean = ( 19 + 22 + 19 + 18 + 22 + 19 + 19 + 19 + 21 + 19 + 44 + 55 + 21 + 22) = 22 (approximately)
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Median:
- To find the median, first, sort the dataset: {18, 19, 19, 19, 19, 19, 19, 19, 21, 21, 22, 22, 22, 44, 55}.
- The median is the middle value. Since there are 14 numbers (an even count), the median will be the average of the 7th and 8th values.
- Median = (19 + 19) / 2 = 19.
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Mode:
- The mode is the number that appears most frequently in the dataset.
- Here, 19 appears 7 times, while others appear less frequently. Thus, the mode is 19.
Comparing these measures:
- The mean is affected by the outliers (44 and 55), which might skew it higher.
- The median is less affected by outliers and represents the middle value well.
- The mode identifies the most frequent value, which is also 19.
Given this dataset has outliers, the median might be considered the best measure of center as it is more representative of the main cluster of values.
So, the best measure of center for this dataset is median.