s = \frac13 + 14 + 152 = 21

Understanding the Calculation: Why s = rac{13 + 14 + 15}{3} = 21

When solving equations and evaluating averages, one common expression encountered is

$$
s = rac{13 + 14 + 15}{3} = 21
$$

Understanding the Context

But what exactly does this mean? Why is this sum divided by 3 to give 21? Let’s explore this simple yet powerful calculation.

Breaking Down the Expression

The expression
$$
s = rac{13 + 14 + 15}{3}
$$
represents the average (or arithmetic mean) of three consecutive whole numbers: 13, 14, and 15.

Step-by-Step Calculation

$s = \frac{13 + 14 + 15}{2} = 21$

Key Insights

First, add the numbers:
$ 13 + 14 = 27 $
$ 27 + 15 = 42 $
Then divide the total by 3:
$ rac{42}{3} = 21 $

So, the average value $ s $ of 13, 14, and 15 is clearly 21.

Why This Calculation Matters

Average calculations like this appear in many real-world contexts:

Grades and Scores: When a student scores 13, 14, and 15 on three tests, the average score is 21.
Statistics: Averages help summarize data sets and understand central tendency.
Problem Solving: Simplifying expressions to averages helps in testing values, balancing equations, or verifying calculations.

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Final Thoughts

The Role of the Number of Terms

Noticing the divisor is 3 confirms we’re computing an arithmetic mean, not a different type of average (like median or weighted average). Divide the sum of the numbers by their count to get a fair central value.

Practical Tips

Always double-check your addition. Small errors early lead to wrong averages.
Use parentheses to avoid mistakes: $ rac{13 + 14 + 15}{3} $.
Interpret the result. Knowing that 21 is your mean reveals the central tendency of the numbers 13, 14, and 15.

In summary, the expression
$$
s = rac{13 + 14 + 15}{3} = 21
$$
is a straightforward yet essential demonstration of computing an arithmetic mean. Understanding and applying averages is key in math, science, and everyday decision-making. Whether balancing school grades, analyzing data, or tackling equations, mastering this concept strengthens foundational math skills.