How to read the spread of a set of figures

This section walks through what the spread numbers on the annualized revenue panel describe, using the two miners named in the fold as the concrete case.

We start with the values. There are 16 miners with annualized revenue on file, out of 18 in the full universe. CleanSpark's annualized revenue is $766.3M. MARA Holdings' annualized revenue is $699.5M. A miner that is not on file is not read as a zero; it is simply absent from the sample.

The panel reports eight spread values for those 16 miners:

• Sample mean: $324.8M
• Median: $239.4M
• First quartile: $81.1M
• Third quartile: $666.8M
• Smallest value: $9.8M
• Largest value: $766.3M
• Sample variance: 8.49 x 10^16 dollars squared
• Sample standard deviation: $291.4M

Now we build each one from the raw values, one operation at a time.

The mean.

Add all 16 annualized revenue values together. Divide the sum by 16. The result is the sample mean: $324.8M.

It is the centre of gravity of the sample. If you balanced all 16 values on a number line, this is where the line would tip.

The variance, and why the divisor is the count less one.

For each of the 16 miners, subtract the sample mean from its value. Square the difference. Do this for every miner. Add the 16 squared differences together.

Now divide. The divisor is not 16. It is 15.

The result is the sample variance: 8.49 x 10^16 dollars squared.

Why the count less one? It looks like an odd choice, but the reason is short. The sample mean was computed from the same 16 values. That pulls the mean toward the data, so the squared deviations from it are, on average, a little smaller than the squared deviations from the population mean would be. Dividing by 15 instead of 16 corrects that shrinkage when the observed values are treated as a sample.

The standard deviation.

Take the square root of the sample variance.

$291.4M

The result is the sample standard deviation: $291.4M. It puts the spread back in the same units as the revenue values, so it can be read alongside them directly.

The quartiles.

Arrange all 16 values from smallest to largest.

The first quartile, $81.1M, is the value below which one quarter of the sample falls.

The median, $239.4M, is the value below which half the sample falls.

The third quartile, $666.8M, is the value below which three quarters of the sample falls.

The smallest value on file is $9.8M. The largest is $766.3M.

Together, the quartiles split the ordered sample into four groups of equal size. A miner's position within those groups is an order by size, nothing more.

Recap.

The mean and the median mark where the centre of the sample sits. The standard deviation measures how far, on average, a value in the sample sits from that centre. The quartiles divide the ordered sample into four equal parts, so the position of any one miner within the spread is a matter of rank, not of judgement.