What was the standard deviation of this problem:Tim scored 59 on a Year 7 numeracy test, which was 1 standard deviation below the mean. On the same test, Francis scored 77, which was 2 standard...

What was the standard deviation of this problem:

Tim scored 59 on a Year 7 numeracy test, which was 1 standard deviation below the mean. On the same test, Francis scored 77, which was 2 standard deviation above the mean.

Asked on by tamanimat

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

Let m and s be the mean and standard deviation.

Then by data,

Tim's score : m-s = 59

Francis' score: m+2s = 77

Francis' score -Tim's score: m+2s-(m-s) =77-59

=> 3s = 18

=> 3s/3 = 18/3

=> s = 6.

Substitute s = 6 in the first equation: m-6 = 59 

=> m = 59+6 = 65.

The standard deviation = 6. The mean = 65.

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