Sampling Distributions The following data represent the ages of the winners of the Academy Award for Best Actor for the years 2012–2017.

a. Compute the population mean, mu.

Verified step by step guidance

1. Identify the data points representing the ages of the winners: 55, 44, 33, 41, 41, and 59.
2. Recall that the population mean \( \mu \) is calculated by summing all the data points and then dividing by the total number of data points.
3. Write the formula for the population mean: \[ \mu = \frac{\sum_{i=1}^N x_i}{N} \] where \( x_i \) are the individual ages and \( N \) is the total number of winners.
4. Calculate the sum of the ages: add 55 + 44 + 33 + 41 + 41 + 59.
5. Divide the sum obtained by the number of winners (which is 6) to find the population mean \( \mu \).

Key Concepts

Population Mean (μ)

The population mean is the average of all values in a population. It is calculated by summing all data points and dividing by the total number of points. In this context, it represents the average age of all Best Actor winners from 2012 to 2017.

Data Collection and Population Definition

Understanding what constitutes the population is crucial. Here, the population includes all Best Actor winners from 2012 to 2017. Correctly identifying the population ensures accurate calculation of parameters like the mean.

Summation and Division in Mean Calculation

Calculating the mean involves two steps: summing all individual data values and dividing by the number of values. This process transforms raw data into a single representative value, simplifying analysis and comparison.