If the mean of y1 and y2 is M1
and
that of y1, y2, y3, y4 is M2,
the mean of ay1, ay1.y3/a, y4/a is
To find the mean of ay1, ay1.y3/a, y4/a, we need to calculate the sum of all the values and divide it by the total number of values.
Let's break down the given expression step by step.
ay1: This is simply a scalar 'a' multiplied by y1. So, the mean of ay1 would be a times the mean of y1, which is M1. Therefore, the first term contributes 'a * M1' to the overall mean.
ay1.y3/a: Here, we have 'ay1.y3' in the numerator and 'a' in the denominator. The 'a' in the denominator cancels out with the 'a' in the numerator, leaving y1.y3. So, the mean of this term is the mean of y1.y3.
y4/a: This term is 'y4' divided by 'a'. So, the mean of this term is the mean of y4 divided by 'a'.
To calculate the overall mean, we need to find the sum of all the terms and divide it by the total number of terms, which is 3 in this case.
Overall mean = (a * M1 + mean of y1.y3 + mean of y4/a) / 3
Therefore, the answer to the question is (a * M1 + mean of y1.y3 + mean of y4/a) / 3.