Find the arithmetic mean of the first ten odd natural numbers.

To find the arithmetic mean of the first ten odd natural numbers, we first need to identify what those numbers are. The sequence of odd natural numbers starts from 1 and continues as 1, 3, 5, 7, 9, 11, 13, 15, 17, and 19. Now, let’s break down the steps to calculate the arithmetic mean.

Identifying the First Ten Odd Natural Numbers

The first ten odd natural numbers are:

• 1
• 3
• 5
• 7
• 9
• 11
• 13
• 15
• 17
• 19

Calculating the Sum

Next, we need to find the sum of these numbers. Adding them together gives:

• 1 + 3 = 4
• 4 + 5 = 9
• 9 + 7 = 16
• 16 + 9 = 25
• 25 + 11 = 36
• 36 + 13 = 49
• 49 + 15 = 64
• 64 + 17 = 81
• 81 + 19 = 100

So, the total sum of the first ten odd natural numbers is 100.

Finding the Mean

The arithmetic mean is calculated by dividing the sum of the numbers by the total count of the numbers. In this case, we have:

Mean = Total Sum / Number of Values

Substituting the values we have:

Mean = 100 / 10 = 10

Final Result

The arithmetic mean of the first ten odd natural numbers is 10.

Understanding the Concept

The arithmetic mean is a measure of central tendency that gives us an idea of the average value in a set of numbers. In this case, the mean of 10 indicates that if we were to distribute the total sum of these odd numbers evenly, each number would represent 10. This concept is widely applicable in various fields, from statistics to everyday life, helping us summarize data effectively.