For each student in a certain class, a teacher adjusted the student's test score using the formula y = 0.8x + 20, where x is the student's original test score and y is the student's adjusted test score. If the standard deviation of the original test scores of the students in the class was 20, what was the standard deviation of the adjusted test scores of the students in the class?
A. 12
B. 16
C. 28
D. 36
E. 40
[spoiler]OA=B[/spoiler]
Source: Official Guide
For each student in a certain class, a teacher adjusted
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Hi Vjesus12.VJesus12 wrote:For each student in a certain class, a teacher adjusted the student's test score using the formula y = 0.8x + 20, where x is the student's original test score and y is the student's adjusted test score. If the standard deviation of the original test scores of the students in the class was 20, what was the standard deviation of the adjusted test scores of the students in the class?
A. 12
B. 16
C. 28
D. 36
E. 40
[spoiler]OA=B[/spoiler]
Source: Official Guide
Before making any computation let's take into account the following result:
(1) If we add a number to all the data of a set \(S\), then the standard deviation of the set \(S\) doesn't change, that is to say, the standard deviation of the new data will be the same of the set \(S\).
(2) If we multiply all the data of a set \(S\) by a number \(k\), then the standard deviation of the new data will be the standard deviation of \(S\) multiplied by \(k\).
Now, we know that \(x\) represents the original test score of the students and \(y\) is the student's adjusted test score.
Since \(y=\color{green}{0.8}x+\color{red}{20}\) we can conclude, using the facts written above, that the standard deviation of the adjusted test scores of the students in the class is equal to the standard deviation of the original test score multiplied by \(\color{green}{0.8}\).
On the other hand, we are told that the standard deviation of the original test scores of the students in the class was 20. Then, the standard deviation of the adjusted test score is $$20\cdot0.8=16.$$ Therefore, the correct answer is the option _B_.
I hope it is clear. <i class="em em-sunglasses"></i>
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Let's review two rules for the standard deviation: 1. Adding a constant to each value in a data set does not change the value of the standard deviation; 2. Multiplying each value in a data set by a constant also multiplies the standard deviation by that constant.VJesus12 wrote:For each student in a certain class, a teacher adjusted the student's test score using the formula y = 0.8x + 20, where x is the student's original test score and y is the student's adjusted test score. If the standard deviation of the original test scores of the students in the class was 20, what was the standard deviation of the adjusted test scores of the students in the class?
A. 12
B. 16
C. 28
D. 36
E. 40
[spoiler]OA=B[/spoiler]
Source: Official Guide
Thus, for y = 0.8x + 20, we see that adding 20 does not affect the value of the standard deviation. But multiplying each score by 0.8 means that the standard deviation of the entire data set is also multiplied by 0.8; thus, the standard deviation of the adjusted test scores will be 20 x 0.8 = 16.
Answer: B
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