How Much Variation Is There Between Low and High Performers in Different Countries?
The variation between low and high performers within countries provides important contextual information to understand average assessment results by providing a measure of the range or inequality of scores within a country. A common way to examine such variation is to measure the difference between cutpoint scores at the 10th and 90th percentiles for a particular subject area. The cutpoint score at the 10th percentile is the highest score achieved by the bottom 10 percent of students and the cutpoint score at the 90th percentile is the lowest score achieved by the top 10 percent of students.
Figures A-1 and A-2 show the dispersion of PISA 2006 mathematics literacy scores for 15-year-olds at the 10th and 90th percentiles. These are arranged by jurisdiction from smallest to largest gap and are shown separately for the OECD and non-OECD jurisdictions. Among the OECD countries, the differences in cutpoint scores ranged from 208 in Finland to 270 in Belgium, with the United States at 234 and an OECD average of 235. Among the non-OECD jurisdictions, the differences in cutpoint scores ranged from 117 in Azerbaijan to 277 in Israel.
As shown in figures A-1 and A-2, there is no consistent relationship between a country's average score and the variation between its low-performing 15-year-olds (i.e., those scoring at or below the 10th percentile) and high-performing 15-year-olds (i.e., those scoring at or above the 90th percentile) in mathematics literacy. Some countries with relatively high average scores have a relatively large gap between their low and high performers (e.g., Chinese Taipei and Switzerland), while others have a relatively small gap (e.g., Finland and Canada). Similarly, some countries with relatively low average scores have a relatively large gap between their low and high performers (e.g., Argentina and Bulgaria), while others have a relatively small gap (e.g., Indonesia and Mexico).
Finland and Chinese Taipei were among the highest-performing countries in mathematics literacy. Fifteen-year-olds in these two countries (along with Korea and Hong Kong–China) scored higher, on average, than all other countries on the mathematics literacy scale but did not measurably differ from each other. However, the relationship of low and high performers in each country was different. In Finland, the cutpoint scores at the 10th and 90th percentile were 444 and 652, respectively, for a difference of 208 points. In Chinese Taipei, the cutpoint scores at the 10th and 90th percentile were 409 and 677, respectively, for a difference of 268 points. Thus, relative to Finland, the high overall average score of 15-year-olds in Chinese Taipei can be attributed more to the performance of its very high performing students; whereas Finland's high average score can be attributed more to the performance of students across the distribution of low to high performing students.