Find arithmetic means (to include: calculating the means for two…

The idea

The mean is the total of the scores divided by how many scores there are. In an experiment, it is calculated separately for each condition to allow comparison. With eight participants recalling 7, 9, 12, 6, 10, 8, 11 and 9 words in the quiet condition, the total is 72 and the mean is 9.0 words. With 5, 4, 8, 6, 7, 5, 9 and 8 words in the noisy condition, the total is 52 and the mean is 6.5 words, a gap of 2.5 words in favour of quiet. Divide by the number of scores in that condition, never by the total number of people in the study, and keep the unit on the answer. Because every score is used, the mean is the most sensitive measure of central tendency, which is why one extreme score can drag it away from the bulk of the data.

What earns the marks

• The method written as a method: add all the scores in one condition, then divide by the number of scores in that condition. Write the sum out rather than only the final figure to show the working clearly.
• Two conditions, two calculations: the answer sentence compares them, for example the mean number of words recalled was 9.0 in the quiet condition and 6.5 in the noisy condition, a difference of 2.5 words.
• Units and precision: quote the result in the unit of the original measure and to an appropriate number of decimal places, typically one more than the raw data, so 6.5 words is acceptable and 6.500 words is not.

Common mistakes and how to put them right

• Adding the totals of both conditions and dividing by all the participants, which produces one overall figure and answers a question nobody asked.

• Letting the divisor drift away from the data, by including a participant who withdrew or by treating a score of zero as no score at all and dividing by a smaller number.

• Leaving the unit off, so a figure such as 6.5 sits on the page with nothing to say whether it counts words, seconds or errors.

• Reporting the answer to five decimal places because that is what the calculator displayed.

Exam tips

• The data always arrive in a printed table, so put the total on the page first to demonstrate the initial step of the calculation.
• A calculation is frequently followed by an instruction to say what the two figures show, which asks for the size and direction of the difference and not for a claim about statistical significance.
• Check whether the question wants the result for each condition or for each participant group, because the two are not the same when group sizes are unequal.