A population consist of multiple of five numbers where is 5, 10, 15, 20, 25, and 30 with sample size of 2. Find the population mean.

1. Break Down the Problem

To find the population mean, we first need to understand the components involved. The population consists of the following numbers: 5, 10, 15, 20, 25, and 30. The sample size given is 2, which does not affect the calculation of the population mean, as the mean is derived from all members of the population.

2. Relevant Concepts

The formula for calculating the population mean $\mu$ is given by: $\mu = \frac{1}{N} \sum_{i=1}^{N} x_i$ where:

• $N$ is the total number of elements in the population.
• $x_i$ are the elements of the population.

3. Analysis and Detail

1. Identify the population: The population is {5, 10, 15, 20, 25, 30}.

2. Count the number of elements in the population: $N = 6$

3. Calculate the sum of the population elements: $\sum_{i=1}^{N} x_i = 5 + 10 + 15 + 20 + 25 + 30 = 105$

4. Apply the mean formula: $\mu = \frac{1}{6} \times 105 = 17.5$

4. Verify and Summarize

We have calculated the mean of the entire population, confirming that it includes all the numbers in the defined set. The calculated sum and subsequent division yield the population mean accurately.

Final Answer

The population mean is $\mu = 17.5$.