s = \frac13 + 14 + 152 = 21 - Coaching Toolbox
Understanding the Calculation: Why s = rac{13 + 14 + 15}{3} = 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
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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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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.
