Answer :
In this problem, we are presented with a sample of size n=10, and we are provided with the sample mean, ž, which is equal to 13.5. Additionally, we are introduced to a new variable Y, which is defined as Y=x+3, where x represents the original data points. Our task is to calculate the mean of Y, represented by žY.
Let's first understand the concept of the transformation Y=x+3. When we apply this transformation to each data point in the original sample, we are effectively adding 3 to every value. This means that every data point in the new variable Y will be 3 units greater than its corresponding value in the original sample.
The mean of a sample represents the average value of all data points in the sample. Therefore, the mean of Y, žY, will be the average value of all the data points in the new variable Y, considering the transformation Y=x+3.
To find žY, we simply need to add 3 to the original sample mean ž. Mathematically, it can be expressed as follows:
žY = ž + 3
= 13.5 + 3
= 16.5
So, the mean of Y, žY, is equal to 16.5.
In conclusion, we have determined that the mean of the new variable Y, which is defined by the transformation Y=x+3, is 16.5. This means that on average, the data points in the new variable Y are 16.5 units greater than their corresponding values in the original sample.
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