The Standardised Score

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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.

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