Standard error of average daily trade count

Question

An analyst records the number of trades executed each day over $n = 36$ days. The sample standard deviation of the daily counts is $s = 12$ trades.

What is the standard error of the average daily trade count?

Accepted Answer

Any single day's trade count swings around a lot (spread of about 12), but the average over many days is much more stable. The standard error of the mean quantifies that stability. Divide the day-to-day spread by the square root of the number of days: 	ext{SE} = \frac{s}{\sqrt{n}} = \frac{12}{\sqrt{36}} = \frac{12}{6} = 2 	ext{ trades}. So the average daily trade count is nailed down to within about 2 trades, even though individual days vary by roughly 12. Takeaway. The standard error of the mean is the daily spread divided by \sqrt{n}: averaging over 36 days shrinks the noise sixfold.

Standard error of average daily trade count

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