Collecting and processing data practice questions.

A student times each of twelve hockey players over 20 m three times instead of once. What does the extra data collection make possible?

• A mean and a measure of spread for every player
• Removal of the calibration fault in the timing gates
• Control of the independent variable during the test
• An increase in the number of participants in the study from twelve to thirty-six

Answer: A mean and a measure of spread for every player

Repeats belong to one participant, so they yield a mean and a spread (range or standard deviation) for that participant; they do not create extra participants and they cannot correct a gate that is wrongly calibrated, because that fault shifts every repeat in the same direction.

A squad completes three 20 m sprints each and the results are entered in a table. Which entry is processed data?

• The time displayed by the timing gate for the second sprint
• The mean of one athlete's three sprint times
• The body mass of each athlete read from the scales
• The air temperature recorded in the sports hall before testing began

Answer: The mean of one athlete's three sprint times

Processed data are values calculated from raw values, such as a mean, a percentage or a per-kilogram figure; everything read directly from an instrument stays raw, however carefully it was measured.

A student tabulates the heart rate of cyclists during the final minute of each stage of a submaximal test. Which column heading follows the data table convention?

• Mean heart rate, with bpm written after each value in the column
• Heart rate 152 bpm
• Mean heart rate / bpm
• The mean heart rate of the participant in the final minute

Answer: Mean heart rate / bpm

The heading names the quantity and states the unit once, so every cell can hold a bare number; repeating the unit in each cell or hiding a single reading in the heading makes the column impossible to process or plot.

A jump mat used with a volleyball squad resolves to 0.1 cm. Which set of entries is correct for the raw column headed 'Jump height / cm'?

• 38.04, 39.53, 41.19, 40.41
• 38, 39.5, 41.15, 40
• 38.0 cm, 39.5 cm, 41.2 cm, 40.4 cm
• 38.0, 39.5, 41.2, 40.4

Answer: 38.0, 39.5, 41.2, 40.4

Raw values are recorded to the precision the instrument actually resolves, with the same number of decimal places down the whole column and no unit in the cells; extra digits claim a resolution the mat does not have.

Mean vertical jump height for each of four netball squads is plotted with error bars of plus or minus one standard deviation. What do those bars show?

• The spread of the individual jumps about each mean
• The difference between the highest and the lowest squad mean recorded
• The uncertainty in the mean of the four squad values
• The number of players who were tested in each of the squads

Answer: The spread of the individual jumps about each mean

An error bar of one standard deviation describes how widely the individual results scatter about their own mean, which is why two squads with the same mean can look very different; it is not the range between the squad means, not the uncertainty of the overall mean and not the sample size.

In a three-trial agility test one time is 18.9 s while the other two are 12.4 s and 12.6 s, and the tester saw the participant slip. How should the 18.9 s value be treated?

• Replace the value with the mean of the other two trials so the set of three stays complete
• Keep it in the raw table but leave it out of the mean, giving the reason
• Delete the value from the raw table before any processing is done
• Report the median of the three trials without mentioning the slip

Answer: Keep it in the raw table but leave it out of the mean, giving the reason

Raw data are never altered or deleted; an outlier with an identified cause is kept in the raw table, flagged, and excluded from the processed value with the reason stated so that a reader can judge the decision.