IB Physics Uncertainty & Error Bars (+ Chemistry, Biology) IA

IA data analysis: uncertainties. This answer loses the mark.

The student took the stopwatch, plus or minus zero point zero one. Can you see the mistake?

Your three trials spread from two point three one to two point three five. Half that range is zero point zero two. So it's plus or minus zero point zero two.

That's one mark of this six-mark data quiz. Five more, and none of them is the obvious answer.

So why does the stopwatch lose? And what do you do with that zero point zero two next?

Your stopwatch reads to a hundredth of a second. But your hand doesn't. Your reaction time changes every trial. That's why your three trials don't agree.

The spread of your trials shows the real uncertainty. When it's bigger than the instrument's uncertainty, you use the bigger one. Same rule in biology and chemistry: a pipette, a balance, a ruler. In your processed data table, you write the mean, plus or minus half the range, with the units in the column heading.

Next, the percentage uncertainty. You divide the uncertainty by the value, and multiply by a hundred. Zero point zero two over two point three three. About zero point nine percent. Mark two.

Why bother? Because a percentage lets you compare. Your timing was much better than one percent. And percentages carry through your calculations. Work out g from your period, and T is squared, so its percentage uncertainty doubles. About one point seven percent. So where does that zero point zero two go on your graph?

Every point on your graph gets an error bar. It goes up by the uncertainty, and down by the uncertainty. Your graphing software can draw them for you, but you choose the values.

So for two point three three, plus or minus zero point zero two. How long is the whole bar? Zero point zero two, zero point zero four, or two point three three?

Zero point zero four. From two point three one up to two point three five. Mark three. And here's what the bars tell you. If your best-fit line passes through them, your scatter is explained by your uncertainty. Now, would you catch a mistake in someone else's table?

You're the examiner now. Three students wrote down the same mean. One mark is for the uncertainty. One mark is for the decimal places.

Student A has too many digits, and the stopwatch uncertainty. Zero. Student B has the right uncertainty, but four decimal places. One mark. Student C has both. Two marks.

So here's the rule. Your value stops at the same decimal place as its uncertainty. A value can't be more precise than its own uncertainty. Two point three three, plus or minus zero point zero two. Mark four. But a table of correct numbers still isn't a conclusion. What do you compare it with?

This was a pendulum, one point three metres long. Theory predicts a period of two point two nine seconds. Your result runs from two point three one to two point three five. Does it agree?

No. Two point two nine is outside your range. Even with the uncertainty, the gap doesn't close. So your conclusion says that, honestly. It compares your result with the accepted value, and it says whether your uncertainty covers the gap. Mark five.

So if the gap is bigger than your uncertainty, what caused it? Pause if you want to try it first; here it is.

Random errors scatter your results both ways. This gap goes one way: every period is too long. That's a systematic error. Here, the string was measured to the top of the bob, not to its centre. So the real length is longer, and so is the period.

Your evaluation names that weakness, says how it pushed your results, and gives a realistic fix. Measure the length to the centre of the bob. Mark six. And for the random error, time ten swings, then divide by ten. Your reaction time is then shared across ten periods.

Uncertainty of a mean? Half the range. Decimal places? Same as the uncertainty. A gap bigger than the uncertainty? A systematic error.

Your data is solid. So which statistical test do you need for a biology IA? That's part two.