Chapter 8.1, Problem 16PSB

To determine

To calculate:The location of arithmetic mean and geometric mean of the numbers on given number line.

Answer to Problem 16PSB

The position of arithmetic mean is P, at 10th place on given number line

The position of Geometric mean is Q, at 8.5th place on given number line

Explanation of Solution

Given information A number line with the marked points 5 and 15

Formula used Arithmetic mean (A.M.) of numbers A and B is $\frac{A+B}{2}$

Geometric mean (G.M.) of numbers A and B is $\sqrt{A.B}$

Calculation:

  

The A.M. will be

  $\begin{array}{l}=\frac{5+15}{2}\\ =10\end{array}$

And

G.M.

  $\begin{array}{l}=\sqrt{5\times 15}\\ =\sqrt{75}\\ =5\sqrt{3}\\ =5\times 1.7\\ =8.5\end{array}$