Question

What is the arithmetic mean (average) of Set A? (A) 41 (B) 60 (C) 71 (D) 142

Short answer

The arithmetic mean of Set A is 78.5, which is not among the given choices. The problem appears to be incomplete or incorrect.

Step-by-step solution

Add the values in Set A

First, find the total of all values in Set A: 41 + 60 + 71 + 142.

Determine the number of values in Set A

There are 4 values in Set A.

Calculate the arithmetic mean (average)

Divide the total of values in Set A by the number of values: \(\frac{41 + 60 + 71 + 142}{4}\).

Simplify the expression

By simplifying the expression, we get: \(\frac{314}{4}\).

Perform the division

When we perform the division, we get the mean value of Set A: 78.5. In this multiple-choice problem, the arithmetic mean (78.5) is not found among the choices (A) 41, (B) 60, (C) 71, and (D) 142. The problem seems incomplete or incorrect as presented.

Key concepts

Average Calculation

To find the arithmetic mean, also called the average, you need to add up all the numbers in a set and divide by how many numbers there are. This gives you a single value that represents the center of the data set.

• Start by adding all the numbers together to get the total.
• Count how many numbers you added together—that is your divisor.
• Divide the total by the number of values to find the average.

For example, to find the average of Set A: 1. **Addition**: Add 41, 60, 71, and 142, which equals 314.2. **Division**: Divide 314 by the 4 values in Set A. Thus, the average is \(\frac{314}{4} = 78.5\).Calculating the average can provide a quick understanding of the overall trend or value in a collection of numbers.

Problem Solving

Problem-solving is about recognizing what is asked and applying the correct methods to find the answer. In this arithmetic mean problem, understanding each step's purpose is vital. Here's how you tackle it:

• Identify the objective: Calculate the mean of four numbers.
• Follow a systematic approach: adding numbers, counting them, and dividing.
• Interpret results to check for errors or reasonableness, like seeing if the mean fits the given choices.
• Consider special cases, such as when options don't match the calculated result.

An important step in problem-solving is verification. If your calculated mean isn't among provided options, recheck each step. Mistakes in addition or division are common. Alternatively, the problem might have an error or need amending.

Mathematics Education

Learning mathematics involves not only memorizing formulas but understanding concepts like the arithmetic mean. It's crucial for students to:

• Comprehend underlying principles of calculations.
• Gain confidence through consistent practice.
• Apply arithmetic mean to real-world scenarios, like finding average scores or costs.

A strong mathematics education helps students develop critical thinking skills. Techniques such as breaking down complex problems into smaller steps and verifying results enhance problem-solving abilities. Educators often encourage students to discuss their mathematical reasoning with peers and instructors to deepen understanding. Teaching should focus on both procedural knowledge and conceptual understanding. Together, these elements make math more than just numbers and formulas—it becomes a tool for navigating everyday challenges.