A Family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family? 

A Family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?

To find the average age of the family, you can add up the ages of all family members and then divide by the total number of family members.

Let's denote the ages as follows:

• Grandparent 1: G1
• Grandparent 2: G2
• Parent 1: P1
• Parent 2: P2
• Grandchild 1: C1
• Grandchild 2: C2
• Grandchild 3: C3

Now, we know the average ages:

• Average age of grandparents (G1 and G2): 67 years
• Average age of parents (P1 and P2): 35 years
• Average age of grandchildren (C1, C2, and C3): 6 years

We also know the family structure:

• 2 grandparents
• 2 parents
• 3 grandchildren

Now, we can set up the following equations based on the information given:

1. (G1 + G2) / 2 = 67 (average age of grandparents)
2. (P1 + P2) / 2 = 35 (average age of parents)
3. (C1 + C2 + C3) / 3 = 6 (average age of grandchildren)

Now, we can express the total family age and the total number of family members:

Total family age = G1 + G2 + P1 + P2 + C1 + C2 + C3 Total number of family members = 2 (grandparents) + 2 (parents) + 3 (grandchildren) = 7

Now, let's substitute the average age equations into the total family age equation:

Total family age = 2 * 67 + 2 * 35 + 3 * 6

Now, calculate the total family age and then find the average age:

Total family age = 134 + 70 + 18 = 222

Average age of the family = Total family age / Total number of family members = 222 / 7 ≈ 31(5/7) = 31.71 years

So, the average age of the family is approximately 31.71 years.

What is an Average?

In mathematics, the term "average" can refer to several different ways of summarizing a set of numbers. However, the most common type of average is the mean, which is calculated by adding all the numbers in the set and then dividing by the number of numbers.

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Here's a breakdown of the different types of averages:

Mean: This is the most common type of average and is calculated by the following formula:

Mean = (Σx_i) / n

where:

• Σ (sigma) represents the sum of all the values in the set.
• x_i represents each individual value in the set.
• n represents the total number of values in the set.

Median: The median is the "middle" value in a set of numbers when arranged in ascending or descending order. If there are an even number of values, the median is the average of the two middle values.

Mode: The mode is the most frequent value in a set of numbers. It can be useful for identifying the most common value, but it doesn't necessarily represent the "typical" value in the set.

Here are some additional points to remember about averages:

• The mean is sensitive to outliers, meaning that a single very large or small value can significantly affect the average.
• The median is less sensitive to outliers than the mean.
• The mode is not very informative if there are no clear "most frequent" values.
• The choice of which average to use depends on the specific data and what you want to summarize.