Question

The ages of a group of people are: 34, 27, 36, 18, 15, 72, 67, 12, 24, 45. What percentage of people in the group are above the average age for the group?

Hint:

When calculating the percentage of values 'above' or 'below' an average, be careful not to include values that are exactly equal to the average.

Answer 1

Step 1: Understanding the Question:
The problem asks for two main calculations: first, find the average age of the group, and second, determine what percentage of the people in the group have an age greater than this average.
Step 2: Key Formula or Approach:
1. Average (Mean): \[ \text{Average} = \frac{\text{Sum of all values}}{\text{Number of values}} \] 2. Percentage: \[ \text{Percentage} = \left( \frac{\text{Number of people above average}}{\text{Total number of people}} \right) \times 100\% \] Step 3: Detailed Explanation:
Part 1: Calculate the average age
The given ages are: 34, 27, 36, 18, 15, 72, 67, 12, 24, 45.
Total number of people = 10.
Sum of ages = \(34 + 27 + 36 + 18 + 15 + 72 + 67 + 12 + 24 + 45\).
Sum of ages = 350.
Average age = \(\frac{350}{10} = 35\) years.
Part 2: Calculate the percentage of people above the average age
The average age is 35. We need to count how many people are older than 35.
Let's check the ages:
34 (not above), 27 (not above), 36 (above), 18 (not above), 15 (not above), 72 (above), 67 (above), 12 (not above), 24 (not above), 45 (above).
The ages above 35 are 36, 72, 67, and 45.
Number of people with age above average = 4.
Now, calculate the percentage:
Percentage = \(\left( \frac{4}{10} \right) \times 100\%\)
Percentage = \(0.4 \times 100\% = 40\%\).
Step 4: Final Answer:
40\% of the people in the group are above the average age.