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Question: If \(y = - 8x - 5\) and SD of \(x\) is 3, then SD of \(y\) is: A.8 B.24 C.3 D.None of these...

If y=−8x−5y = - 8x - 5 and SD of xx is 3, then SD of yy is:
A.8
B.24
C.3
D.None of these

Explanation

Solution

As we know, SD stands for standard deviation. The standard deviation basically represents the measure of how spread out our data is or how spreads out numbers are. It is represented by a geek symbol σ\sigma . Now, we can calculate the standard deviation by taking square root of variance. So, we need to know what variance is. The variance is the average of squared differences of given data from mean. And we all know the mean is the total value divided by the number of values. In this way we can find out the standard deviation. It is given in the question that standard deviation of xx is 3. The equation of yy is given in terms of xx . So, we can easily calculate standard deviation on both sides of the equation and we can find out the standard deviation of yy .

Complete step-by-step answer:
It is given in the question that the standard deviation of xx is 3.
We can write it as σ(x)=3\sigma \left( x \right) = 3 .
The equation of is given to be y=−8x−5y = - 8x - 5
Now, applying standard deviation to the both sides of the equation, we get
⇒σ(y)=σ(−8x−5) ⇒σ(y)=σ(−8x)+σ(−5)  \Rightarrow \sigma \left( y \right) = \sigma \left( { - 8x - 5} \right) \\\ \Rightarrow \sigma \left( y \right) = \sigma \left( { - 8x} \right) + \sigma \left( { - 5} \right) \\\
We know that σ(c)=0\sigma \left( c \right) = 0 , so equation becomes
⇒\Rightarrow σ(y)=σ(−8x)+0\sigma \left( y \right) = \sigma \left( { - 8x} \right) + 0
Also, σ(aX)=∣a∣σ(X)\sigma \left( {aX} \right) = \left| a \right|\sigma \left( X \right)
Therefore, equation will be
⇒σ(y)=8σ(x) ⇒σ(y)=8×3=24  \Rightarrow \sigma \left( y \right) = 8\sigma \left( x \right) \\\ \Rightarrow \sigma \left( y \right) = 8 \times 3 = 24 \\\
So, the standard deviation of yy is 24.
Hence, option B is correct.

Note: As we know, attention is needed to do these types of questions because we have to take a lot of values in calculation and we cannot make mistakes in the values. The calculation of standard deviation should also be rechecked to avoid any mistakes in these types of questions.