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When working with averages, one important value to understand is the total sum of items being considered. In our exercise, this involves calculating the total sum of ages of the group of people. To calculate the total sum of ages, multiply the mean (average age) by the total number of individuals. This relationship can be expressed as: \[ \text{Total Sum} = \text{Mean} \times \text{Number of People} \] In this specific problem, the group has a mean age of 46 years for six people. We find the total sum of their ages as follows: \( 46 \text{ years} \times 6 = 276 \text{ years} \) This calculation gives us the sum of all six ages combined, which is a foundational step in finding any unknown value.

Solving statistics problems often involves breaking down complex information into manageable steps. In this problem, we follow certain steps to find the unknown age among a group of people. Once we have the total sum of all ages, the next step is essential. Calculate the sum of ages for the known values. This involves simply adding together the ages we know. 馃摑 **Steps for Solving**:

• Identify the known data: In our example, these are the five ages: 57, 39, 44, 51, and 37.
• Add these ages together: \( 57 + 39 + 44 + 51 + 37 \).
• Compute the sum: \( 228 \text{ years} \).

Understanding these initial steps sets a clear foundation to solve the problem accurately. By organizing each part, you ensure that nothing is overlooked, aiding in achieving a correct, thoroughly thought-out solution.

Once you have gathered the known information, the next step is to uncover the unknown value鈥攊n this case, the age of the sixth person. This is where elementary algebra skills come in handy. 馃暤锔� **Solving for the Unknown**:

• Start by determining the total sum you previously calculated for all ages: 276 years.
• Subtract the sum of the known ages from the total sum: \( 276 - 228 \).
• The result gives you the age of the sixth person, which in this exercise is 48 years.

This method of finding the unknown through subtraction from the total sum is a useful technique in many statistics problems, providing clarity and precision when uncovering missing information.