The Standardized Score

The standardized score is a statistical tool thatallows comparison of related quantities that are normallydistributed. A very good use is test scores. When a student wishes tocompare their own results with everybody elses, they may stanaridizetheir scores to find the percentile in which they lie.

Suppose one student recorded his marks in a set ofexams and collected the mean and standard deviation of all the othermarks of the other students.

The standard score is given by

For mathsFrom tables, 72.57% of scores were lower.

For englishFrom tables, 59.87% of scores were lower.

For physicsFrom tables, 62.8% of scores were lower.

For chemistryFrom tables, 97.72% of scores were lower.

For biologyFrom tables, 79.49% of scores were lower.

In order of decreasing performance his results were chemistry,biology, maths, physics and english.