Questions: The data in the table represent the ages of the winners of an award for the past five years. Use the data to answer questions (a) through (e) 60 25 41 47 44 9 (a) Compute the population mean, μ μ= (Type an integer or a decimal)

The data in the table represent the ages of the winners of an award for the past five years. Use the data to answer questions (a) through (e)

60 25
41 47
44 9

(a) Compute the population mean, μ
μ= (Type an integer or a decimal)

Transcript text: The data in the table represent the ages of the wnners of an award for the past five years. Use the data to answer questions (a) through (e) \begin{tabular}{rl} 60 & 25 \\ \hline 41 & 47 \\ \hline 44 & 9 \end{tabular} (a) Compute the population mean, $\mu$ $\boldsymbol{\mu}=$ $\square$ (Type an integer or a decimal)

Solution

Solution Steps

Step 1: Data Collection

The ages of the winners of the award for the past five years are given as follows: \[ \{60, 25, 41, 47, 44, 9\} \]

Step 2: Calculation of the Population Mean

To compute the population mean $ \mu $, we use the formula: \[ \mu = \frac{\sum_{i=1}^N x_i}{N} \] where $ N $ is the total number of data points and $ x_i $ represents each individual data point.

Step 3: Summation of Ages

Calculating the sum of the ages: \[ \sum_{i=1}^N x_i = 60 + 25 + 41 + 47 + 44 + 9 = 226 \]

Step 4: Number of Data Points

The total number of data points $ N $ is: \[ N = 6 \]

Step 5: Mean Calculation

Substituting the values into the mean formula: \[ \mu = \frac{226}{6} \approx 37.67 \]