# Quick data guide

## Centile scores

A centile score (sometimes referred to as a ‘percentile score’) should not be confused with percent correct. It reflects a student’s ability on any given test on a scale of 1 to 99 in comparison with other students in the reference group (i.e. the norm group or the same age group). Hence the average student will obtain centile scores in the middle range (e.g. in the range 35–65), whilst an above-average student will have centile scores higher than this, and the below-average student will have centile scores lower than this. For example, a student with a centile score of 5 will be

just inside the bottom 5% of students for that particular ability, and a student with a centile score of 95 will be just inside the top 5% of students for that particular ability.

## Z-scores

A z-score (also known as a standard deviation unit) is a statistic based on a normal distribution of scores. Most human characteristics are distributed in a normal (or approximately normal) fashion (i.e. a bell shaped curve), in which individuals cluster towards the mean (or average) and become less common as one approaches the extremes (or ‘tails’) of the distribution. The proportion of individuals that will fall in any given portion of a normal distribution can be calculated. For example, two-thirds (66%) of individuals will lie between + or – one standard deviation of the mean, while slightly less than 3% will fall below 2 standard deviations of the mean.

## Relationship between centile scores and z-scores

In a normal distribution of scores, centile scores and z-scores have a consistent relationship to each other and also to standard scores, (the latter, like IQ, being most usually expressed with a mean of 100 and a standard deviation of 15). This relationship is depicted below.

 centile score 3 5 17 20 25 50 75 83 97 z-score –2.0 –1.75 –1.0 –0.85 –0.66 0 0.66 1 2 standard score 70 76 85 87 90 100 110 115 130