Math Problem Statement

((35-372,37299)^22200+(75-372,37299)^23000+(125-372,37299)^212000+(175-372,37299)^225000+(250-372,37299)^230000+(350-372,37299)^228000+(450-372,37299)^216300+(550-372,37299)^23200+(650-372,37299)^210100+(750-372,37299)^29200+(850-372,37299)^25900+(950-372,37299)^22800+(1050-372,37299)^2*1900)/149600

Solution

To solve this expression step-by-step, let's simplify it carefully. We need to compute each term within the summation, then add them up, and finally divide by 149600. Here’s the detailed approach:

Expression

((35372.37299)2×2200+(75372.37299)2×3000+(125372.37299)2×12000++(1050372.37299)2×1900)149600\frac{((35 - 372.37299)^2 \times 2200 + (75 - 372.37299)^2 \times 3000 + (125 - 372.37299)^2 \times 12000 + \ldots + (1050 - 372.37299)^2 \times 1900)}{149600}

Step 1: Calculate (xi372.37299)2(x_i - 372.37299)^2 for each term

Calculate each (xi372.37299)2(x_i - 372.37299)^2 for:

  • x1=35x_1 = 35
  • x2=75x_2 = 75
  • x3=125x_3 = 125
  • \ldots
  • x13=1050x_{13} = 1050

Step 2: Multiply each result by the corresponding coefficient

For each term, after finding (xi372.37299)2(x_i - 372.37299)^2, multiply by the weights:

  • 2200,3000,12000,,19002200, 3000, 12000, \ldots, 1900

Step 3: Sum all these products

Add the results from Step 2.

Step 4: Divide by 149600

Finally, divide the sum by 149600 to obtain the final result.

Let’s calculate this precisely.The result of the expression is approximately:

54340.9954340.99

Would you like further details on any part of the calculation, or have any questions?

Here are some related questions that might interest you:

  1. How does changing the denominator affect the result?
  2. What if we changed the weights in each term—how would that impact the overall sum?
  3. Why is it necessary to square the difference in each term?
  4. How would the result change if the constant was different?
  5. How could this type of calculation be applied in statistics?

Tip: When dealing with large expressions, breaking down each component step-by-step helps prevent errors and ensures accuracy.

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Math Problem Analysis

Mathematical Concepts

Algebra
Statistical Analysis
Squares and Summation

Formulas

Summation of weighted squared differences
Weighted average formula

Theorems

Pythagorean Theorem (as it involves squares of differences)
Statistics: Weighted Mean

Suitable Grade Level

Grades 11-12