$$ \sqrt{\frac{\sum\left(4282-428.2\right)^2}{9}} $$

To solve the given expression:

\[
\sqrt{\frac{\sum(4282 - 428.2)^2}{9}}
\]

Let's break it down step by step:

### Step 1: Simplify inside the summation
You are summing $ (4282 - 428.2)^2 $, but since there is no indication of multiple terms in the summation, we can assume this is applied to a set of values. However, without specific values given, let's first calculate this difference:

\[
4282 - 428.2 = 3853.8
\]

### Step 2: Square the result
Now, square $ 3853.8 $:

\[
3853.8^2 = 14852520.44
\]

### Step 3: Divide by 9
Now divide the squared result by 9:

\[
\frac{14852520.44}{9} = 1650279.493
\]

### Step 4: Take the square root
Finally, take the square root of $ 1650279.493 $:

\[
\sqrt{1650279.493} \approx 1284.67
\]

So the value of the given expression is approximately **1284.67**.

Would you like to see more details or clarifications? Here are some related questions:

1. What is the significance of the summation symbol in statistical contexts?
2. How do you interpret this formula as a standard deviation calculation?
3. Can this expression represent a variance calculation?
4. How would adding more terms to the summation affect the result?
5. How do you handle summations involving variable numbers of terms?

**Tip**: Always carefully distinguish between the different steps in summations and apply proper operations at each stage!

Learn how to solve a summation-based problem involving the square root of variance using detailed step-by-step guidance. This problem breaks down algebraic operations, square root calculations, and variance formulas, suitable for students in Grades 9-11.

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