Question

If each element in a data set is multiplied by 3, and each resulting product is then reduced by 4, which of the following expressions gives the mean of the resulting data set in terms of x?

a. x
b. 3x-4
c. x+4/3
d. x/3+4
e. x+4/3

Answer 1

The mean of the transformed data set, if each element in the original set is multiplied by 3 and then reduced by 4, is given by 3x bar - 4. This reflects the application of the function f(x) = 3x - 4 to the original mean of the data set. So the correct answer is option B.

Step-by-step explanation:

If each element in a data set is multiplied by 3, and each resulting product is then reduced by 4, the transformation applied to every data value x is represented by the function f(x) = 3x - 4.

Now, to find the mean of the transformed data set, let's consider the original mean of the data set, represented as x with a bar over it (x bar). The original mean is the sum of the original data values divided by the number of data values. When we apply the transformation to the entire data set, each data value x is replaced with 3x - 4. Therefore, the mean of the new data set will likewise be transformed by the same function applied to the original mean.

The new mean, in terms of the original mean x bar, is therefore 3x bar - 4 (Option b).