Question

Compare the quantity in Column A and the quantity in Column B. Then determine whether:

A. the quantity in Column A is greater;

B. the quantity in Column B is greater;

C. the two quantities are equal;

D. the relationship cannot be determined from the information given.

23.

The average (arithmetic mean) of $\text{s}$ and $\text{t}$ is greater than the average of $\text{s}$ and $\text{w}$

Column A Column B

$\text{w}$ $\text{t}$

Short answer

The quantity in Colum B is greater than the quantity in Column A. So,the correct option isB.

Step-by-step solution

- Consider the two quantities.

The average (arithmetic mean) of s and t is greater than the average of s and w.

The quantity in column A is:

$w$

The quantity in column B is:

$t$

- Evaluate the two quantities.

Average is defined as sum of the observations divide by the number of observation.

The average of $s$and $t$is $\frac{s+t}{2}$.

And the average of s and w is $\frac{s+w}{2}$.

Now, since $\frac{s+t}{2}>\frac{s+w}{2}$, then,

$\begin{array}{c}\frac{s+t}{2}>\frac{s+w}{2}\\ \frac{s+t}{2}\times 2>\frac{s+w}{2}\times 2\\ s+t>s+w\\ s+t-s>s+w-s\\ t>w\end{array}$

Thus, $t>w$that is quantity in column B is greater than quantity in column A.

- State the conclusion.

The quantity in column B is greater than quantity in column A. Therefore, option B is correct.