Lesson 5 of 6
Practical skills: tables, graphs and errors
I can choose and explain measuring instruments and methods with suitable range and precision, including the linked quantity-specific determinations.Syllabus
Syllabus K223 / K224, 1(e). Choose and explain measuring instruments and methods with suitable range and precision, including the linked quantity-specific determinations.
Make a guess. You are not marked.
You time 10 swings of a pendulum three times and get 12.6 s, 12.4 s and 12.8 s. What value should you record for the time of 10 swings?
Show the answer
12.6 s, the mean of the three readings.
Repeated readings scatter because of reaction time. Their mean, (12.6 + 12.4 + 12.8) / 3 = 12.6 s, is the best value to record.
In short
- Record readings in a table, with the quantity and its unit in each column heading.
- Plot the quantity you changed on the x-axis and the quantity you measured on the y-axis.
- Draw a smooth best-fit line or curve through the points, not dot to dot.
Exam questions about practical work often ask you to record readings, complete a table, read a graph or suggest an improvement. These habits earn those marks.
1. Record each reading to the precision of the instrument
Write every reading to the smallest division or display step of the instrument you used. A rule marked in millimetres reads to 0.1 cm, so a length that ends exactly on the 12 cm mark is 12.0 cm, not 12 cm. For a digital instrument, write exactly what the display shows.
| Instrument | Record to | Example |
|---|---|---|
| Metre rule (mm markings) | 0.1 cm | 45.0 cm |
| Digital calipers | 0.01 mm, as displayed | 12.34 mm |
| Digital stopwatch | 0.01 s, as displayed | 15.62 s |
| Digital ammeter or voltmeter | Every digit displayed | 0.38 A |
Readings from one instrument should have the same number of decimal places all the way down a column.
2. Draw the table so that it can be marked
- Heading = quantity / unit. Write l / cm or R / Ω at the top of each column. Put units only in the heading, never next to each number.
- Take at least 5 sets of readings. Spread them evenly over the widest range the apparatus allows.
- Repeat and average when readings vary, for example timing a swing or a falling object. Keep the raw readings in the table as well as the mean.
3. Plot a graph the way it is marked
- Plot the right way round. "Plot R against l" means R goes up the vertical axis and l goes along the horizontal axis.
- Label both axes with the quantity and unit, written the same way as the table heading, such as R / Ω.
- Choose an easy scale. Let each large square stand for 1, 2 or 5 units (or 10, 20, 50 and so on). Never use 3, 6 or 7: these make points hard to plot and read.
- Fill at least half the grid in both directions. The axes do not need to start at zero unless the question asks for it.
- Plot each point carefully, to within half a small square, as a small cross or a dot with a circle round it.
- Draw one thin line of best fit. Use a ruler for a straight line, or draw one smooth curve. Leave about as many points above the line as below it. Never join the dots point to point.
4. Name a real source of error and a matching improvement
"Human error" or "repeat the experiment" on its own scores nothing. Name the specific problem, say how it affects the reading, and give an improvement that fixes that problem.
| Source of error | Matching improvement |
|---|---|
| Reaction time is large compared with the time of one swing. | Time 20 oscillations and divide by 20. |
| Parallax when reading a scale from an angle. | Place the eye directly in line with the mark, perpendicular to the scale. |
| The wire heats up, so its resistance rises during the experiment. | Use a small current and open the switch between readings. |
| The hot liquid loses energy to the surroundings. | Insulate the beaker and cover it with a lid. |
Check your understanding
A student measures the length of a spring with a metre rule marked in millimetres. The spring ends exactly at the 12 cm mark. How should she record the length in her table?
Show the answer
12.0 cm
The rule is marked in millimetres, which is 0.1 cm. So record every reading to 0.1 cm, even when the last digit is zero.