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The teacher recorded the mean and median of the hourly wage for each student. Unfortunately, he forgot to label them. The numbers he wrote down were: $11.25/hour and $9.38/hour. Which would be the mean and which would be the median?

A) The mean is $9.38/hour. The median is $11.25/hour.
B) The mean is $11.25/hour. The median is $9.38/hour.
C) This cannot be determined from the information given.

1 Answer

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Final answer:

The most likely scenario for the hourly wage numbers presented is that the higher value represents the mean and the lower value represents the median, due to the mean's sensitivity to high outliers. Therefore, the mean is likely $11.25/hour and the median is $9.38/hour. The correct option, considering typical wage distributions, is B.

Step-by-step explanation:

The mean and median are measures of central tendency that describe the center of a data set. The mean is the average of all the data points, while the median is the middle value when all the data points are ordered from least to greatest. When there is a symmetrical distribution of data, the mean and median are equal. However, in a skewed distribution, such as when we see outliers or a non-uniform distribution, the mean can be overly influenced by extreme values, while the median remains a more robust measure of the central tendency.

Given that the two numbers recorded are $11.25/hour and $9.38/hour, without additional context we cannot definitively determine which is the mean and which is the median. However, typically in a normal wage distribution, it is more common for the mean wage to be higher than the median wage because the mean can be pulled higher by exceptionally high wages - a characteristic of being sensitive to outliers. As such, the most likely scenario is that B) the mean is $11.25/hour, and the median is $9.38/hour.

In conclusion, the correct option, given typical wage distributions, is B.

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