To determine the best measure of central tendency for the salaries of the workers in the store, let's calculate the mean, median, and mode, and also consider whether the interquartile range is relevant.
The weekly salaries are: $82, $79, $84, $300, and $78.
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Mean: \[ \text{Mean} = \frac{82 + 79 + 84 + 300 + 78}{5} = \frac{623}{5} = 124.6 \]
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Median: First, we need to arrange the salaries in ascending order: $78, $79, $82, $84, $300. The median is the middle value in this ordered list, which is $82.
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Mode: The mode is the value that appears most frequently. In this case, there are no repeating values, so there is no mode.
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Interquartile Range: The interquartile range measures the spread of the middle 50% of the data; however, it does not directly indicate the typical wage.
Given these calculations:
- The mean is $124.6, but this is significantly affected by the outlier ($300).
- The median is $82, which represents the middle salary and is less influenced by the outlier.
- There is no mode.
Thus, the median is the best measure of central tendency to describe the typical wage of a worker in this store, as it effectively represents the central point of the majority of the salaries without being skewed by the outlier.
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