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Summation is a fundamental concept in mathematics and is often used in statistics for analyzing data sets. In simple terms, summation is the process of adding a sequence of numbers. The symbol used to denote summation is \( \Sigma \), which is the Greek letter Sigma. This symbol signifies that you are summing up values according to a specified rule.

In the given problem, we are tasked with summing the products of a set of values and a constant, specifically summing \( 0.1 x_i \) for each \( x_i \) in our list of numbers. The formula used is \( \Sigma(a x_i) = a(x_1 + x_2 + x_3 + ... + x_n) \). This is a reflection of the distributive property, which states that multiplying a sum by a number yields the same result as multiplying each addend individually by the number, and then summing up all those products. This is an efficient way to handle operations involving summation and multiplication.

Arithmetic operations form the foundation of most mathematical computations, including those in statistics. The primary operations include addition, subtraction, multiplication, and division. In this exercise, multiplication and addition are key.

For each of the values given, we performed a simple multiplication by the constant 0.1, which involved calculating:

• \( 0.1 \times x_1 = 0 \)
• \( 0.1 \times x_2 = 0.29 \)
• \( 0.1 \times x_3 = 0.55 \)
• \( 0.1 \times x_4 = 0.08 \)
• \( 0.1 \times x_5 = 0.31 \)

After computing the products, the summation follows: all products are added together to achieve the final answer, \( 1.23 \). This process illustrates the real-world application of arithmetic in solving problems and analyzing data sets.

Data analysis involves examining, cleaning, transforming, and modeling data with the goal of discovering useful information, arriving at conclusions, and supporting decision-making. In this exercise, the focus is on a small data set which is part of a larger strategy to understand and interpret data.

When dealing with any data set, we first identify and understand each data point's role in addressing the problem at hand. Here, the data points \( x_1, x_2, x_3, x_4, x_5 \) are manipulated through multiplication, and their sum provides insight into their collective behavior when scaled by 0.1.

Through these steps, simple data analysis can be performed that reveals trends or patterns, indicating how the data behaves under certain mathematical transformations. This analysis, though basic, is foundational for more complex statistical analysis, which can involve various techniques including measures of central tendency, dispersion, correlation, and more intricate mathematical operations.