## 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.

Subject | Score, | Mean, | Standard Deviation, |

Maths | 78 | 72 | 10 |

English | 80 | 83 | 12 |

Physics | 65 | 70 | 15 |

Chemistry | 80 | 60 | 10 |

Biology | 79 | 65 | 17 |

The standard score is given by

For mathsFromtables, 72.57% of scores were lower.

For englishFromtables, 59.87% of scores were lower.

For physicsFromtables, 62.8% of scores were lower.

For chemistryFromtables, 97.72% of scores were lower.

For biologyFromtables, 79.49% of scores were lower.

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