Mean, Mode, Median: The Other 3M
- theangryactuary
- Oct 12, 2023
- 2 min read
One of the things that really ticks me off is when people in a financial services setting don't understand basic statistics. If we want to estimate the total premium in a market, we'd multiply the average premium per policy (mean) by the total number of policies. But one genius suggested that we use the median premium instead. Apparently, fudging it for convenience was high on his agenda. Cue my internal Mount Vesuvius...
Mean:
This is more commonly known as the average. Pretty basic. If you want the mean, just add up all the individual numbers and then divide by how many numbers you have. Simples...
Median:
In a group of numbers, this is the point where half the numbers are below and half the numbers are above. So if we have a median income of £40,000 a year, this means that 50% of people earn less and 50% of people earn more. This can be a better measure of general earnings because an average in this case would likely be higher as mega earners will skew the mean calculation.
Mode:
Popularity: it even exists in statistics. The mode is simply the most common value. For example, with a set of numbers: 1, 1, 2, 2, 3, 3, 3, 3, 4, 5, 5, there are more instances of 3, hence, it is the mode. It is possible to have a bi-modal or even multi-modal distribution where more than one of the values has the most common occurrence.
Finally, for a standard normal distribution, also known as the bell curve, the three above are actually all the same thing:
In closing, make sure you know the three M's. It's not hard and it will definitely help you fake it till you make it. It will also piss people off less.
Further reading (dare I say homework?):
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