To help all y'all understand life better: median, mean (average), and mode

Rabrrrrrr

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Sat Mar-10-07 01:24 PM
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To help all y'all understand life better: median, mean (average), and mode

Edited on Sat Mar-10-07 01:26 PM by Rabrrrrrr

Sadly, journalism today sucks and is so dumbed down as to be practically without value, and so asshole writers are always giving us shit for statistical analyses. So, I offer you this helpful guide:

Mean (in non-statistical terms, "average")

One you are surely familiar with: whatever the numbers are, add them all up, divide that total by the number of numbers, and voila - the average.

The mean, however, rarely ends up in the center of the numerical range.

For example, let's use the "Average wedding cost is $28,000". That phrase actually gives the world absolutely no useful information. We are no smarter knowing that information than we were not knowing it. When someone says something like that to you, your response should be "So what? That number has no meaning because you gave it no context."

If five wedding samples were taken, it could have been the cost for the five were: $26K, $27K, $28K, $29K, and $30K. That averages to $28K, which in this case, is right in the middle. But that $28K average also could come from a sample of 10 weddings that had a cost of $10K for 9 of them, and a cost of $190K for one of them. Or 100 weddings that cost $2000 for 99 of them, and one that cost $2,602,000.

See how saying "Average is $28K" offers no information of any value?

Median

The median is that number which is in the exact center of the lineup of numbers under question. In my first example, it's $28K. In the second example, it's $10K, and in the third it's $2000.

In the list of numbers $3K $5K $9K $50K $73K (mean is still $28K), the median is $9K, because it's in the center. In the list of number $2K $3K $3K $9K $50K $101K (still maintaining our mean of $28K), the median is the average of the middle two (3 and 9) which is $6K.

mode

The number that shows up most frequently. In my first example, none of them are the mode. In the second, it's $10K since it appears 9 times, and in the third it's $2000 since it shows up 99 times. In the two lists of numbers above, the first list has no mode (every number appears only once) and the second list's mode is $3K.

range

Range is merely the difference between the lowest number and the highest number. Some statisticians add 1 to that total. There seems to be debate on it.

In the first example, the range is $5K; the second is $180K, and the third is $2,600K. In the two lists of numbers, the range of the first is $70K, and the second is $99K.

conclusion

So, hopefully, you can see how utterly devoid of information the phrase "average cost of wedding is $28,000".

Example 1: mean=$28K, range=$5K, median=$28K, mode=empty
Example 2: mean=$28K, range=$180K, median=$10K, mode=$10K
Example 3: mean=$28K, range=$2600K, median=$2K, mode=$2K
Example 4: mean=$28K, range=$70K, median=$9K, mode=empty
Example 5: mean=$28K, range=$99K, median=$6K, mode=$3K