Question

The average of \(1000.0001,100.001,10.01,1.1\) is : (a) \(277.777\) (b) \(322.222\) (c) \(11.11\) (d) \(233.333\)

Short answer

Answer: (a) 277.777

Step-by-step solution

Sum of the given numbers

First, we need to calculate the sum of the given numbers: \(1000.0001 + 100.001 + 10.01 + 1.1\). Summing up these numbers, we get: \(1111.1111\).

Calculate the average

Now, we need to divide the sum by the total number of values, which is 4. So, the average will be: \( \frac{1111.1111}{4}\) Dividing \(1111.1111\) by 4, we get: \(277.777775\)

Compare the options

Let's compare our computed average to the given answer options: (a) \(277.777\) (b) \(322.222\) (c) \(11.11\) (d) \(233.333\) Our computed average is \(277.777775\), which is closest to option (a) \(277.777\). So, the correct answer is:

Answer

(a) \(277.777\)

Key concepts

Arithmetic Mean

Understanding the concept of the arithmetic mean, commonly referred to as the average, is crucial to many fields, not just math. In the context of the provided exercise, the arithmetic mean is used to find the central value of a set of numbers by dividing the sum of these numbers by their quantity.

When you see a series of numbers such as 1000.0001, 100.001, 10.01, and 1.1, the arithmetic mean helps to summarize this data into a single, informative value. It's particularly useful because it gives a sense of the 'middle' of the data, even if the numbers are very spread out, as they are in this example.

The process of finding the mean is straightforward and involves two main steps: summing up all the numbers, and then dividing by the count of the numbers. It's expressed mathematically as: \[ \text{Arithmetic Mean} = \frac{{\text{Sum of values}}}{{\text{Number of values}}} \].

In our case, a correct summation of the numbers and then dividing by 4 (since there are 4 values) leads to the right answer. Remember that accuracy in the initial arithmetic is vital to ensure a correct final result.

Quantitative Aptitude

Quantitative aptitude involves the ability to handle numbers and perform mathematical operations and is invaluable in everyday problem solving. It encompasses various math topics, including arithmetic operations, algebra, geometry, and data interpretation. For students trying to master these problems, it's important to not just follow the steps mechanically, but to understand the principles behind them.

Being proficient in quantitative aptitude means being able to approach numerical problems logically and efficiently. It's not just about having math skills; it's about applying those skills in practical situations, such as calculating averages in the provided example.

To bolster your quantitative aptitude, consistently practice different types of math problems, and when tackling something like an average calculation, pay close attention to details like decimal places and the correct order of operations. These practice sessions build upon the foundation of quantitative reasoning, enabling students to approach their homework or standardized tests with confidence.

Problem-Solving

Problem-solving is as much about adopting the right strategy as it is about the execution of mathematical operations. Effective problem-solving involves several stages: understanding the problem, devising a plan, carrying out the plan, and checking the results.

In the context of our exercise, problem-solving begins with accurately interpreting what's required—in this case, calculating the average of a set of numbers. The next phase is planning and executing the necessary arithmetic operations properly. Finally, we need to verify our worked-out answer against the given options, choosing the most appropriate one.

Developing good problem-solving skills requires practice and a willingness to make mistakes and learn from them. For a typically numerical problem like finding an average, it's also helpful to estimate the answer before beginning the math, to provide a ballpark figure that your calculated answer should fall into. This kind of estimation can quickly highlight any potential errors in the calculation process before arriving at the final answer.