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Let's go through the problem step by step. The given data are \( x_1 = 2 \), \( x_2 = 5 \), \( x_3 = 3 \), and \( x_4 = 4 \). We are asked to calculate the following sums:

### a) \( \sum_{i=1}^4 x_i \)
This sum is just the sum of all the given \( x_i \):
\[
\sum_{i=1}^4 x_i = x_1 + x_2 + x_3 + x_4 = 2 + 5 + 3 + 4 = 14
\]

### b) \( \sum_{i=1}^4 8 \)
This is a constant sum where each term is 8:
\[
\sum_{i=1}^4 8 = 8 + 8 + 8 + 8 = 32
\]

### c) \( \sum_{i=1}^4 2x_i \)
Here, each term is multiplied by 2:
\[
\sum_{i=1}^4 2x_i = 2(x_1) + 2(x_2) + 2(x_3) + 2(x_4) = 2(2) + 2(5) + 2(3) + 2(4) = 4 + 10 + 6 + 8 = 28
\]

### d) \( \sum_{i=1}^4 (x_i - 3) \)
This involves subtracting 3 from each \( x_i \):
\[
\sum_{i=1}^4 (x_i - 3) = (2 - 3) + (5 - 3) + (3 - 3) + (4 - 3) = (-1) + 2 + 0 + 1 = 2
\]

### e) \( \sum_{i=1}^4 x_i^2 \)
Here we square each \( x_i \):
\[
\sum_{i=1}^4 x_i^2 = 2^2 + 5^2 + 3^2 + 4^2 = 4 + 25 + 9 + 16 = 54
\]

### f) \( \sum_{i=1}^4 (x_i - 3)^2 \)
We first subtract 3 from each \( x_i \) and then square the result:
\[
\sum_{i=1}^4 (x_i - 3)^2 = (2 - 3)^2 + (5 - 3)^2 + (3 - 3)^2 + (4 - 3)^2 = (-1)^2 + 2^2 + 0^2 + 1^2 = 1 + 4 + 0 + 1 = 6
\]

### Summary of the results:
- a) \( \sum_{i=1}^4 x_i = 14 \)
- b) \( \sum_{i=1}^4 8 = 32 \)
- c) \( \sum_{i=1}^4 2x_i = 28 \)
- d) \( \sum_{i=1}^4 (x_i - 3) = 2 \)
- e) \( \sum_{i=1}^4 x_i^2 = 54 \)
- f) \( \sum_{i=1}^4 (x_i - 3)^2 = 6 \)

Would you like further details or explanations on any step? 

Here are five related questions to deepen your understanding:
1. What is the general form of a summation and how can it be simplified?
2. How do constant sums like in part (b) affect the total sum?
3. What is the importance of squaring terms in a summation?
4. How would the results change if different values for \( x_i \) were provided?
5. Can you think of real-world scenarios where such summations are useful?

**Tip:** When solving summations, simplify step by step to avoid errors, especially when variables or constants are involved.

Misalkan empat hasil pengukuran dalam suatu himpunan data adalah x1 = 2 ; x2 = 5 ; x3 = 3 ; dan x4 = 4. Hitunglah nilai-nilai numerik penjumlahan berikut:
a) Σxi 
b) Σ8 
c) Σ2xi 
d) Σ(xi - 3) 
e) Σxi^2 
f) Σ(xi - 3)^2

Learn how to solve various summation problems using data x1 = 2, x2 = 5, x3 = 3, and x4 = 4. Explore Σxi, Σ8, Σ2xi, Σ(xi - 3), Σxi^2, and Σ(xi - 3)^2 with step-by-step solutions. Suitable for high school students studying algebra and summations.

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