What does average actually mean?

By Poppy Ionides, Educational Psychologist

The notion of average doesn’t elicit the awe and wonder of high scores or the concern oft associated with low ones, but scores falling in the middle of the range deserve equal examination to those at the extremes. After all, each average score is part of a unique life story for which the future is all to play.

What an average score tells us

The journey of understanding what average scores in psychometric tests do and don’t tell us starts with maths. One might expect a cut and dried answer to the meaning of ‘average’. Interestingly, conventions differ: most test publishers define an average score as one lying within the middle fifty percent of the population (standard scores 90-109*) but those reporting scores do not always choose to define average in this way. For instance, some professionals prefer to think of the average range as the 68% of scores which fall within one standard deviation of the mean (standard scores 85-115). Step one, then, of understanding ‘average’ is to be clear on the definition in operation.

What an average score doesn’t tell us

Maths is just the starting point for making the most out of scores. Two identical scores can hide startlingly different stories. The questions below uncover what scores alone don’t tell us:

Does an average overall score mask significant highs and lows? The CAT4 study reported here suggests that heterogeneity of scores is the rule rather than the exception: four out of five children with an average overall score fell outside the average range for one or more of the verbal, quantitative and spatial domains. Be alive to the possibility – likelihood, even – of spiky areas of strength and difficulty in a child’s skill profile.

Are the child’s scores in line with other evidence about their current abilities and understanding? Remember that scores provide a snap shot of a child’s performance on a particular day; they give a good indication of ability but carry a margin of uncertainty. Consider the possibility of impact from factors such as fear of failure, impulsivity, distractibility, illness, hunger, tiredness and prior learning (including EAL).

Is the child making expected progress? If not:

o Do they see their academic ability as set in stone or a set of skills which can be refined over time? A large body of evidence suggests long-term benefit from a ‘growth mindset’ in which children believe in the possibility of cultivating their abilities. This feeds perseverance and resilience; failures are seen as opportunities to learn rather than diktats of inescapable ineptitude; those who start ‘average’ have the ability to be all but. Schools have the power to influence children’s mindset.

o Are they demotivated? Intrinsic motivation requires the experience of competence, positive relationships and an opportunity to behave in line with our values and interests. Exploring the way in which a child views their competence, relationships, values and interests gives valuable information.

Is there congruence between priorities and beliefs at home and school? Understanding the way in which the child’s family views education will help teachers to narrow any gaps that exist between beliefs held by home and school. When communicating with families, be mindful of the possibility of unintended power hierarchies which leave parents feeling inferior and unheard.

One could argue that the questions above are appropriate for making the most of all scores, not just those in the realm of average. I would agree with that. But for those who sit in the comfort of the mid-range it is often not seen as relevant to look behind and beyond scores. As such, this report gives the perfect context in which to sharpen our thinking on what average scores do and don’t tell us.

*Standard scores compare a child’s performance with the scores achieved by children of their age in the standardisation sample. CAT4 uses standard scores with a mean of 100 and standard deviation of 15. Fifty percent of children achieve standard scores from 90-109; 68% of children achieve standard scores from 85-115.

 

Read more in our new report, The Lost Middle: how the term ‘average’ can obscure student problems and potential