A family with an average age for grandparents of 67, parents of 35, and grandchildren of 6. What's the family's average age?

A family with an average age for grandparents of 67, parents of 35, and grandchildren of 6. What's the family's average age?

In mathematics, the concept of averages is widely used to find a central value among a group of numbers. Here, we'll discuss how to calculate the average age of a family consisting of different age groups, namely grandparents, parents, and grandchildren.

A family has 2 grandparents, 2 parents, and 3 grandchildren.

The average age of the grandparents is 67 years.

The average age of the parents is 35 years.

The average age of the grandchildren is 6 years.

For grandparents:

67 x 2 = 134 years

For parents:

35 x 2 = 70 years

For grandchildren:

6 x 3 = 18 years

Sum up the total ages of all family members

134 + 70 + 18 = 222 years

There are 2 grandparents + 2 parents + 3 grandchildren = 7 family members

Divide the total age by the number of family members

Average age = 222/7 = 31(5/7) years

Concept of Age Based Problems

Calculating the average age in a family or group is a common mathematical problem. It helps to find a central value that represents the entire group. This concept is used widely in various fields, such as statistics, education, and demographics.

Definition of Average:

The average (or mean) is a single value that summarizes a set of numbers. It is calculated by dividing the sum of all the values by the number of values. Let's consider a family consisting of different age groups. For instance, two grandparents, two parents, and three grandchildren. Each group has an average age, and we want to find the overall average age of the entire family.

Steps to Calculate Average Age

• Calculate the total age of the grandparents by multiplying their average age by the number of grandparents.
• Do the same for the parents and grandchildren.
• Add the total ages of all the family members to get the overall sum.
• Count the number of people in each group and sum them up to get the total number of family members.
• Divide the total sum of ages by the total number of family members to get the average age.

Applications

• Averages help in summarizing data. For example, calculating the average age can help understand the age distribution in a group or community.
• Teachers use averages to calculate students' grades and determine overall performance.
• Medical professionals use averages to study the age distribution of patients, which helps in understanding health trends.
• Companies use averages to analyze market trends, such as average customer age, to target their products better.
• Averages simplify complex data sets by providing a single representative number.
• They allow for easy comparison between different groups or time periods.
• Averages help in making informed decisions based on the analyzed data.