Question

The numbers 3.2, 5.8, 7.9 and 4.5 have frequencies Y, (Y + 2), (Y - 3) and (Y + 6), respectively. If the arithmetic mean is 4.876, find the value of Y and write the whole series.

Answer 1

By the definition of the arithmetic mean:

$4.876=\frac{3.2\cdot Y+5.8\cdot(Y+2)+7.9\cdot(Y-3)+4.5\cdot(Y+6)}{Y+(Y+2)+(Y-3)+(Y+6)}$

Let's simplify:

$4.876 = \frac{214Y+149}{40Y+50}$

The solution of the equation is $Y=5$.

So, the numbers 3.2, 5.8, 7.9 and 4.5 have frequencies 5, 7, 2 and 11, respectively.

The whole series: 3.2, 3.2, 3.2, 3.2, 3.2, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 7.9, 7.9, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5.