How many to pin an average?

Sizing a poll for a yes/no split is one thing; pinning down an average ā€” wait time, basket size, blood pressure ā€” is another. Here the lever isn't the proportion, it's the spreadThe standard deviation of the individual values: how spread out they are. Wider spread needs a bigger sample to average out to the same precision. of the values. Feed in how varied they are and how tight a band you want, and read off the sample it takes ā€” or run it backwards.

The precision you want
Pin the average to within Ā±units, at% confidenceHow often the interval contains the true mean across repeated samples. 95% is the default; raising it widens the band, so it costs more..
The values vary with a spread of aboutunits, around a mean near.
Measurements needed
217measurements

Enough to estimate the average to within Ā±2 units ā€” 98 to 102 ā€” at 95% confidence, given a spread of 15.

217measurements
Ā±2target margin
2z usedThe critical z for your confidence level: how many standard errors the margin spans. ā‰ˆ1.96 at 95%, 2.58 at 99%.
MarginMeasurements
Ā±4
55
Ā±2chosen
217
Ā±1
865
Ā±0.5
3,458

Precision costs by the square: the sample grows with (spread Ć· margin)Ā², so halving the band quadruples the measurements. Tightening the last little bit is always the expensive part.

Already collected the data? See the margin it buys ā†’

margin of error for a mean Ā· E = zĀ·Ļƒ/āˆšn