Repeat readings let you spot anomalies (results far from the rest) and take a mean. Leave anomalies out before you average.

mean = sum of the readings ÷ number of readings
uncertainty ≈ ± half the range (range = largest − smallest)

1. Times: 2.34 s, 2.29 s, 2.31 s, 2.38 s
2. mean = 9.32 ÷ 4 = 2.33 s
3. range = 2.38 − 2.29 = 0.09 s
4. uncertainty = ± 0.045 s, so 2.33 ± 0.05 s

Resolution is the smallest change an instrument can show: the gap between marks on a scale, or one in the last digit of a display (0.01 s for 12.46 s).

Significant figures start at the first non-zero digit. Give a calculated answer to the same number of significant figures as the least precise data you used (usually 2 or 3).

0.0450 has 3 significant figures: the zeros at the front never count, the zero at the end after the point does.

• Random error scatters readings both ways by different amounts (reaction time, a flickering display). Reduce its effect by repeating and taking a mean.
• Systematic error shifts every reading the same way by the same amount. Repeating does not help: correct the readings or recalibrate.
• A zero error is a systematic error: the instrument reads something when it should read zero. Take the zero reading away from each reading. In a difference of two readings it cancels.

Precise is not the same as accurate: a balance with a zero error can give readings that agree perfectly and are all wrong.