Problem 6 - Algebra 1: Concepts and Skills

Question

GOLF In Exercises 6 and 7, use the table showing scores for two rounds of golf. $$ \begin{array}{|c|c|c|c|c|} \hline & {\text { Player } 1} & {\text { Player 2}} & {\text { Player 3 }} & {\text { Player 4 }} \\ \hline \text { Round 1} & {90} & {88} & {79} & {78} \\ \hline \text { Round 2} & {94} & {84} & {83} & {80} \\ \hline \end{array} $$ Make a table showing the average score of each player. HINT: Find each average by adding the two scores and dividing by the number of rounds.

Step-by-Step Solution

Answer

The average scores for Player 1 to 4 (in order) are 92, 86, 81, 79.

Step 1: Calculate Average for Player 1

The score for Player 1 in round 1 is 90 and in round 2 is 94. To calculate the average score, add these two scores and divide by the total number of rounds (2 in this case).\nTherefore, the average score of Player 1 is \(\frac{(90+94)}{2} = 92\).

Step 2: Calculate Average for Player 2

The score for Player 2 in round 1 is 88 and in round 2 is 84. Add the two scores and divide by 2 to get the average. The calculation is \(\frac{(88+84)}{2} = 86\).

Step 3: Calculate Average for Player 3

The score for Player 3 in round 1 is 79 and in round 2 is 83. Follow the same process of adding the scores and dividing by 2. The resulting average score is \(\frac{(79+83)}{2} = 81\).

Step 4: Calculate Average for Player 4

Player 4 scored 78 in round 1 and 80 in round 2. To find the average, add these two scores and divide by 2. The average for Player 4 is \(\frac{(78+80)}{2} = 79\).

Step 5: Create the Average Score Table

Finally, make a table similar to the one given in the exercise, replacing the individual round scores with the calculated average scores. Here is the final table: \n \[ \begin{array}{|c|c|c|c|c|} \hline & {\text { Player 1}} & {\text { Player 2}} & {\text { Player 3 }} & {\text { Player 4 }} \ \hline \text { Average Score} & {92} & {86} & {81} & {79} \ \hline \end{array} \]

Key Concepts

Arithmetic Mean

The arithmetic mean is a common way to find the average of a set of numbers. It's a vital concept in mathematics and statistics. To calculate the arithmetic mean, you add together all the numbers in a set, and then divide by the count of the numbers in that set.
For instance, in a golf game where players score different points across rounds, the arithmetic mean helps determine the average score per player. This gives a clear idea of each player's performance over multiple rounds.
Here's a simple breakdown:

• Add up all the scores recorded.
• Divide the total by the number of scores (rounds).

This calculation provides the average score for each player. Understanding this concept is useful not just in sports, but in various fields whenever comparing data across different instances.

Mathematical Operations

Mathematical operations are the processes used to calculate the arithmetic mean. These operations include addition and division.
Addition is the first step where all relevant scores are summed up. For the given scores of each player in two rounds, you start by adding the scores together. For example, Player 1's scores of 90 and 94 are added.
Afterwards, division aids in spreading out the total sum into units per score by dividing the sum by the number of rounds. This provides a fair measure of the performance on average per round, giving you the final result.

• Add scores of all rounds: e.g., 90 + 94 = 184 for Player 1.
• Divide by number of rounds: e.g., 184 ÷ 2 = 92 for Player 1.

These operations are foundational in mathematics and critical for deriving average values.

Data Representation

Data representation involves displaying numbers in a form that's easy to understand. In exercises like golf scores, tables are a great way to visually represent data.
Tables help organize scores from each round and subsequent averages. With columns for each player and rows for rounds and averages, readers can quickly see the performance of players.
The structure ensures clarity, allowing comparisons at a glance. Each player's average is listed under their name, aligned with their scores from specific rounds.

• Clear columns for each player.
• Rows indicating rounds and calculated averages.

Such visual representation simplifies data analysis, making it accessible and easy to interpret.