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7.045 Calculating standard scores

Interactive practice questions

The following table shows the marks obtained by a student in two subjects.

Subject Mark Mean Standard Deviation
Science $100$100 $44$44 $14$14
Math $98$98 $68$68 $15$15
Subject Mark Mean Standard Deviation
Science $100$100 $44$44 $14$14
Math $98$98 $68$68 $15$15
a

How many standard deviations above the mean was the student's score in Science?

b
How many standard deviations above the mean was the student's score in Maths?
c

In which subject was his performance better?

Science

A

Math

B
Medium
1min

Languages and Mathematics are very different disciplines, and so to compare results in the two subjects, the standard deviation is used. The mean and standard deviation of exam results in each subject are given.

Easy
3min

Dylan scored $90%$90% with a $z$z-score of $2$2 in English, and $78%$78% with a $z$z-score of $4$4 in mathematics.

In which subject was his performance better, relative to the rest of his class?

Easy
< 1min

Jenny scored $81%$81% with a $z$z score of $-2$2 in English, and $72%$72% with a $z$z score of $-4$4 in Mathematics. In which subject was her performance better, relative to the rest of the class?

Easy
< 1min
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Outcomes

2.1.6

use the number of deviations from the mean (standard scores) to describe deviations from the mean in normally distributed data sets

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