The standard deviation of x is 3 what is the variance of 5 - 2 x?

Question

Answer

Calculating the Variance of 5 - 2x when the Standard Deviation of x is 3

Understanding Standard Deviation and Variance

Before we dive into the calculation of the variance of 5 - 2x, let's understand what standard deviation and variance mean.

Standard deviation: It is a measure of how spread out the data is from the mean. A low standard deviation indicates that the data is clustered around the mean, while a high standard deviation indicates that the data is more spread out.

Variance: It is the square of the standard deviation. It represents the average of the squared differences from the mean.

Calculating the Variance of 5 - 2x

Now, let's calculate the variance of 5 - 2x when the standard deviation of x is 3.

First, we need to find the variance of x. We know that:

Standard deviation of x = 3

Variance of x = (standard deviation of x)^2 = 3^2 = 9

Now, let's use the formula for the variance of a constant times a random variable:

Var(aX) = a^2 Var(X)

Here, X is the random variable, which is x in our case, and a is a constant, which is -2 in our case.

So, we can write:

Var(5 - 2x) = (-2)^2 Var(x) = 4 Var(x) = 4 * 9 = 36

Therefore, the variance of 5 - 2x is 36.

Conclusion

In conclusion, we can say that the variance of 5 - 2x when the standard deviation of x is 3 is 36. We calculated this by finding the variance of x, using the formula for the variance of a constant times a random variable, and substituting the values in the formula.

Answer

Variance = square of standard deviation

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