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Fashion and Median


Fashion

Fashion is defined as: the value that comes up most often if the data is discrete, or the class interval most often if the data is continuous.

Thus, from the graphical representation of the data, the value that represents the mode or the modal class is immediately obtained.

This is especially useful for reducing information from a qualitative data set, presented in the form of names or categories, for which the average and sometimes the median cannot be calculated.

Median

The median is a measure of the location of the center of the data distribution, defined as follows:

Sorted by the sample elements, the median is the value (belonging or not to the sample) that divides it in half, that is, 50% of the sample elements are less than or equal to the median and the other 50% are greater than or equal to the median. .

For its determination the following rule is used, after ordering the sample of n elements:

If n is odd, the median is the mean element.
If n is even, the median is the semi-sum of the two mean elements.

Average and Median Considerations

As a measure of location, the median is more robust than average because it is not as sensitive to data.

1- When the distribution is symmetrical, the mean and median coincide.
2- The median is not as sensitive as the average to observations that are much larger or much smaller than the others (outliers). On the other hand the average reflects the value of all observations.

As we have seen, the average, unlike the median, is a measure greatly influenced by "very large" or "very small" values, even if these values ​​appear in small numbers in the sample. These values ​​are responsible for the misuse of the mean in many situations where it would be more meaningful to use the median.

From the above, we deduce that if the data distribution:
1. is approximately symmetrical, the mean approximates the median.
2. is skewed to the right (some large values ​​like outliers), the average tends to be greater than the median.
3. skewed to the left (some small values ​​such as outliers), the average tends to be lower than the median.

Next: Dispersion Measures