Final answer:
The appropriate averages for T-shirt color codes are the mode and the median, as they can indicate the most frequently ordered colors and the central trend without the influence of outliers, unlike the mean which reflects skewing the most.
Step-by-step explanation:
If the numbers represent codes for the colors of T-shirts ordered from a catalog, the averages that would make sense are the mode and the median. The mode is useful because it tells us which color was ordered the most frequently, which could be important for inventory and marketing decisions. The median would provide the middle value of the ordered colors when sorted, which could also be useful in identifying central trends without being influenced by extreme values as the mean might be.
In a symmetrical distribution, the mean, median, and mode will all be the same or very close to each other. However, in reality, distributions can be skewed, which will cause the mean to reflect the skewing the most since it is affected by outliers. In such cases, the median or mode might be preferred measures of central tendency, as they are less affected by extreme values.
For example, given the values 45; 47; 47.5; 51; 53.5; 125, the mean is greatly influenced by the outlier of 125, so the median would be a better reflection of the central tendency for the data set. Similarly, the mode would be important for identifying the most common house value in the neighborhood, which again is not influenced by the outlier.