12 FURTHER MATHEMATICS STANDARD SCORES

Standard scores The 68–95–99.7% rule makes the standard deviation a natural measuring stick for normally distributed data. For example, a person who obtained a score of 112 on an IQ test with a mean of 100 and a standard deviation of 15 has an IQ score less than one standard deviation from the mean. Her score is typical of the group as a whole, as it lies well within the middle 68% of scores. In contrast, a person who scores 133 stands out; her score is more than two standard deviations from the mean and this puts her in the top 2.5%. Because of the additional insight provided by relating the standard deviations to percentages, it is common to transform data into a new set of units that show the number of standard deviations a data value lies from the mean of the distribution. This is called standardising and these transformed data values are called standardised or z-scores.

Standard scores

WORK TO BE COMPLETED Exercise 2H All Questions - Summary and Review