Quick questions on Data analysis, error and uncertainty: HSC Investigating Science Module 5

Every measurement has uncertainty arising from instrument resolution and natural variation. Standard ways to report:

Report data with significant figures appropriate to the precision of the instrument.

Sum of values divided by count. The most common measure of central tendency for normally distributed data.

Middle value when data is ordered. Less affected by outliers than the mean.

Difference between maximum and minimum. A simple measure of spread.

A more rigorous measure of spread that quantifies how tightly values cluster around the mean.

Unpredictable variation between repeated measurements, caused by chance fluctuations. Magnitude varies; direction varies. Random error reduces with averaging.

Consistent bias in one direction caused by miscalibration, methodological flaw or biased observer. Systematic error does not reduce with averaging.

Vertical lines showing the range or uncertainty around each data point. Mandatory for any quantitative graph in Investigating Science.

Labelled with quantity and unit. Independent variable on the x-axis, dependent variable on the y-axis. Origin clearly marked.

A class of 30 students measures the period of a pendulum and records times of 1.40, 1.42, 1.41, 1.40, 1.39, 2.10, 1.41 seconds for one student. Identify the outlier using a simple criterion and justify whether it should be excluded. [3 marks]

Annual rainfall at Bourke is reported as 340 plus or minus 60 mm for the 2010s decade and 290 plus or minus 50 mm for the 2020s decade. Comment on whether this constitutes evidence of a drying trend. [3 marks]

A student measures the mass of 10 fresh leaves on a balance reading to 0.01 g. (a) State how to report the uncertainty in a single measurement. (b) Explain how to estimate the uncertainty in the mean.