Recording and Processing Data

Designing a results table — draw the table before you start, so you are not inventing columns with apparatus running. The independent variable goes in the first column, the dependent variable next, and anything you calculate in columns to the right.

Units belong in the heading — write t / s at the top, and every entry beneath it is a plain number. This keeps the table readable, avoids repeating the unit dozens of times, and makes the column easy to process.

Repeats — take at least three readings of each measurement and record every one, not just the mean. Repeats let you calculate an average that reduces the effect of random error, and they make anomalies visible. A single reading gives you no way of knowing whether it is typical.

Anomalies — a reading that plainly does not fit the pattern of the others. Exclude it from the mean, but never delete it: record it, say you excluded it, and suggest why it happened. An unexplained anomaly is a result in itself, and sometimes the most interesting one.

Example: currents of 0.219 A, 0.220 A and 0.193 A at the same p.d. The third does not belong with the other two. The mean of the first two is 0.220 A; including the anomaly would drag it to 0.211 A and misrepresent every subsequent calculation.

Significant figures — count from the first non-zero digit. In 0.00406 the leading zeros are placeholders, so there are three significant figures: 4, 0 and 6.

Significant figures in calculations — a calculated result cannot be more precise than the least precise measurement it came from. Give the answer to the smallest number of significant figures used in the calculation.

Example: 1.2 ÷ 1.85 = 0.648648… on the calculator. But 1.2 is only known to two significant figures, so the answer is 0.65. Writing 0.6486 would claim a precision the measurement of 1.2 never had.

Significant figures are not decimal places — 0.0456 has three significant figures and four decimal places; 123.4 has four significant figures and one decimal place. Round calculated answers to significant figures, and only use decimal places when a question explicitly asks for them.

Means and precision —

mean = sum of the repeated readings ÷ number of readings

Round the mean to the precision of the original readings. If a ruler reads to the nearest millimetre, a mean of 4.2333 cm should be written 4.2 cm. The extra digits are arithmetic, not measurement, and writing them implies an instrument you did not use.

Why this matters outside the classroom — quoting a result to the wrong precision misleads whoever reads it next. An engineer given a cable tension to five significant figures will assume it was measured that carefully, and may design on that basis.