Solution: The arithmetic mean is calculated by summing the values and dividing by the count: $\frac{10 + 14 + 16}{3} = \frac{40}{3} \approx 13.\overline{3}$. The exact average is $\boxed{\dfrac{40}{3}}$.

["Understanding the Arithmetic Mean: A Step-by-Step Calculation", "When analyzing data, one of the most fundamental tools in statistics is the arithmetic mean — commonly known as the average. Whether you’re evaluating exam scores, financial metrics, or scientific measurements, knowing how to calculate the mean accurately helps you interpret data with confidence. This article walks through the simple yet essential process of computing the arithmetic mean, using a clear example to illustrate the method.", "What Is the Arithmetic Mean?", "The arithmetic mean represents the central value of a data set by measuring the balance point of all numbers. It is found by adding together all the values and dividing that total by how many values there are. This measure provides a quick snapshot of the dataset’s overall magnitude.", "How to Calculate the Arithmetic Mean: A Clear Example", "Let’s consider a practical example to explain the steps clearly:", "Suppose we have the values: 10, 14, and 16.", "1. Sum the values:\n Add the numbers together:\n $$\n 10 + 14 + 16 = 40\n $$", "2. Count the values:\n There are three numbers in this dataset.", "3. Divide the total sum by the count:\n $$\n \ ext{Mean} = \frac{10 + 14 + 16}{3} = \frac{40}{3} \approx 13.\overline{3}\n $$", "The exact average is therefore\n$$\n\boxed{\dfrac{40}{3}}\n$$\nwhich, when approximated as a decimal, is approximately 13.33 when rounded to the nearest hundredth.", "Why This Calculation Matters", "Using the arithmetic mean offers a straightforward yet powerful way to summarize data. It serves as the foundation for more advanced statistical analysis, including variance, standard deviation, and regression models. Whether in education, business, or research, knowing how to compute the mean accurately helps ensure reliable conclusions.", "Final Thoughts", "The arithmetic mean is more than just a formula — it’s a critical concept that brings clarity to raw numbers. By following the simple steps of summing values and dividing by count, anyone can calculate the mean and better understand the data they work with.", "So next time you analyze a set of numbers, remember:\n$$\n\ ext{Mean} = \frac{\ ext{Sum of all values}}{\ ext{Number of values}} = \frac{10 + 14 + 16}{3} = \frac{40}{3}\n$$\nand use $\boxed{\dfrac{40}{3}}$ as the exact answer.", "---", "Keywords: arithmetic mean calculation, mean formula, what is arithmetic mean, how to calculate mean, average of numbers, precise mean, sum divided by count, statistical mean example, exact value of mean, $\dfrac{40}{3}$, $\frac{10 + 14 + 16}{3} = \frac{40}{3}$", "---", "This SEO-optimized article clearly explains the arithmetic mean using a real-world example, defines the formula clearly, emphasizes the exact fraction, and includes relevant keywords to improve search visibility for readers studying statistics."]