Suppose a population consists of the values $1$, $8$, $5$, and $6$. What is the population mean?

• A. $4.5$
• B. $5$
• C. $5.5$
• D. $6$

Answer: (C)

Verified step by step guidance

1. Identify the population values given: 1, 8, 5, and 6.
2. Recall that the population mean (\( \mu \)) is calculated by summing all the population values and then dividing by the number of values in the population.
3. Write the formula for the population mean: \[ \mu = \frac{\sum_{i=1}^N x_i}{N} \] where \( x_i \) are the population values and \( N \) is the total number of values.
4. Calculate the sum of the population values: \[ 1 + 8 + 5 + 6 \]
5. Divide the sum by the number of values (which is 4) to find the population mean: \[ \mu = \frac{1 + 8 + 5 + 6}{4} \]