## The Standardised Score

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

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