Question

The table shows a golfer’s scores relative to par for three out of four rounds of a tournament.

The golfer’s goal for the tournament is to have a mean score no greater than $-3$ .Describe how the golfer can achieve this goal.

Scorecard
Round 1	$+1$
Round 2	$-4$
Round 3	$-3$
Round 4	?

Answer 1

Explanation.

We know that, $\mathrm{Mean}=\frac{\mathrm{Sum}\mathrm{of}\mathrm{observation}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{observation}}$

Let $x$ be the score of the golfer in the fourth round.

Here the observations are $1,-4,-3,x$ and the number of observations are $4$.

Given that the mean of the four rounds should be $\le -3$

$\Rightarrow$Mean $\le -3$

$$\begin{gathered} \Rightarrow \frac{(1+(-4)+(-3)+x)}{4}\le -3 \\ \Rightarrow \frac{(-6+x)}{4}\le -3 \\ \Rightarrow -6+x\le -12 \\ \Rightarrow x\le -12+6 \\ \Rightarrow x\le -6 \end{gathered}$$

Therefore, to achieve the goal, a golfer should score less than or equal to $-6$ in the forth round.