Question

Find the mean of the data set. $$ 102,104,106,108 $$

Short answer

Answer: The mean of the data set is 105.

Step-by-step solution

Identifying the values in the data set

The data set consists of four values: 102, 104, 106, and 108.

Calculate the sum of the values

Add the values together: $$ 102 + 104 + 106 + 108 = 420 $$

Determine the number of values

There are four values in the data set, so the number of values is 4.

Calculate the mean

Now, divide the sum of the values (420) by the number of values (4) to find the mean: $$ \frac{420}{4} = 105 $$ The mean of the data set is 105.

Key concepts

Data Set Analysis

When working with statistics, a data set is simply a collection of numbers or values that relate to a particular subject. In our example, the data set is comprised of the numbers 102, 104, 106, and 108.
Analyzing a data set often involves identifying different patterns or trends and extracting key characteristics to understand the data better. Here are some steps to analyze a basic data set:

• Identify the numbers included: Knowing each value helps understand the range and scope of the set.
• Look for patterns: Sometimes there might be sequences or repetitions in the values.
• Check the size: Count how many numbers or values are in the set.

Understanding these aspects can help inform what kind of statistical measures can be useful. Data set analysis is the starting point for a deeper exploration into statistical concepts such as measures of central tendency, like the mean.

Arithmetic Mean

The arithmetic mean is one of the most common statistical measures. It's what people often refer to as the "average."
The arithmetic mean helps summarize a data set with a single representative value. To calculate the mean, follow these steps:

• Sum up all numbers in the data set. For the example data, it would be: 102 + 104 + 106 + 108 = 420.
• Count the number of values in the data set. Our data set contains four numbers.
• Divide the total sum by the number of values: \( \frac{420}{4} = 105 \).

The arithmetic mean tells us that if each number were the same across the board, it would be 105 in this case. The mean is a useful way to get a quick sense of the 'central' value of data.

Statistical Measures

Statistical measures are tools that help us summarize and interpret data sets. They include various concepts designed to highlight different aspects of the data. Here are some common statistical measures:

• Mean: As mentioned earlier, it captures the average value of a data set.
• Median: This tells us the middle value when all numbers are ordered from lowest to highest. It can provide a clearer picture when there are outliers.
• Mode: The most frequently occurring number in a data set, the mode gives insight into the commonality of values.

These measures require an initial understanding of the data set to choose the appropriate type. They allow us to make informed decisions and understand the data more holistically.
By applying different statistical measures, you gain multiple perspectives on the same data, making it easier to spot trends, compare data sets, and draw conclusions.