Problem 31 - Algebra 2

Question

For Exercises \(31-32,\) use the following bowling scores for six members of a bowling team: \(175,210,180,195,208,196 .\) What is the mean of the scores?

Step-by-Step Solution

Answer

The mean of the scores is 194.

Step 1: Sum of scores

Find the sum of the given scores: \(175 + 210 + 180 + 195 + 208 + 196 = 1164\).

Step 2: Count of scores

Count the total number of scores. In this case, there are six scores.

Step 3: Calculate the mean

Divide the sum of the scores found in Step 1 by the total number of scores found in Step 2 to calculate the mean. Thus, the mean is \(\frac{1164}{6} = 194\).

Key Concepts

Understanding Arithmetic Mean

The arithmetic mean is a common way to find the average of a set of numbers. It represents the central value or typical number in a data set. To calculate it, you sum up all the values and then divide by the number of values. This technique helps summarize data into a single informative number that can easily describe the entire set. In our example, the team has bowling scores: 175, 210, 180, 195, 208, and 196. These scores can be combined to find an average score for the team. This average, known as the arithmetic mean, tells us what score is typical or expected within this group. The arithmetic mean is very useful for data comparison and reporting performing trends.

Data Analysis Basics

When we talk about data analysis, we often start by looking at the arithmetic mean. The mean helps us understand the general trend in the data set, especially when comparing multiple sets of data. For instance, in our bowling example, knowing the average score helps compare this team's performance against another team's average score.
Analyzing data like this can reveal:

• Trends over time
• The need for improvement or change in strategy
• Areas of weakness or strength
• Outliers or anomalies in performance

For example, if the team regularly scores around the mean of 194, any score far from it, like a 150 or 250, might be indicative of an irregular performance or highlight an area for review. Data analysis gives a clearer picture of performance and helps with decision-making.

A Step-by-Step Solution Approach

Following a step-by-step solution not only helps in finding the correct answer but also fortifies understanding of the method used. Let's break this down based on the bowling scores we have:
1. **Add the Scores** - Start by adding up all the scores: The scores 175, 210, 180, 195, 208, and 196 amount to 1164 when summed up.2. **Count the Scores** - Determine how many scores you have; in this instance, there are 6 scores. 3. **Calculate the Mean** - Finally, divide the total sum by the count of the scores: So, the mean is \(\frac{1164}{6} = 194\).By breaking down the task in these manageable steps, it becomes easy to replicate this process with different sets of data. Practice these steps regularly for improved confidence in solving similar problems.