Estimate results (to include: commenting on the spread of scores for a set…

The idea

Estimating is a checking skill rather than a shortcut. Round the numbers in a table to something convenient, do the arithmetic in your head, and use the approximate answer to judge whether a calculated figure is plausible, because a mean that falls outside the highest and lowest scores has to be wrong. Dispersion is where examiners ask for this most often: take the largest score and the smallest, subtract, and you have a quick measure of how variable a condition was, so times running from 7 up to 42 seconds vary by about 35 seconds. That measure is crude, since a single extreme score drives it, which is why standard deviation is the figure a researcher reports alongside the mean.

What earns the marks

• Estimating results as a plausibility check: rounding raw data to convenient numbers to mentally calculate an approximate mean or total.
• Estimating the range to comment on the spread of scores: identifying the highest and lowest values in a data set and subtracting them.
• The range stated as a method: the highest score minus the lowest score, written with its unit, so 42 seconds minus 7 seconds is 35 seconds.
• Interpreting the figures rather than only producing them: a small estimated range means scores cluster close together and the condition was consistent, while a large one means participants varied widely.
• Understanding why standard deviation is reported: while the range is easily estimated, standard deviation uses all scores and is not easily calculated mentally, making it a more robust measure of dispersion.

Common mistakes and how to put them right

• Quoting the two end scores, 7 and 42, as the answer instead of the single value 35, or calling the range a measure of central tendency when it measures dispersion.

• Treating two sets with the same range as equally variable, when one outlier has inflated a range that hides tightly clustered scores.

• Estimating where the stem says calculate.

  Put it right: An approximate figure earns nothing when an exact value is asked for, and a calculated value with no working earns nothing if it is wrong.

• Attempting to calculate the standard deviation in an exam when only an estimate of the range or a comment on the spread is required.

Exam tips

• The wording is usually briefly outline what the range tells the researcher about these data. Answer about variability and consistency, never about the average.
• Quote figures from the table when asked to comment on the results: name the condition with the wider spread, give both values, and tie the comparison back to the hypothesis.
• Estimating from a graph counts too. Read the highest and lowest points off the vertical axis, subtract, and state the scale units in the answer.