Find the mean of 10, 8, 5, 11, 12, 9, 6, 3, 15, and 23.

1. Analyze the question

You are asked to calculate the mean (also known as the arithmetic average) of a given set of ten numbers: 10, 8, 5, 11, 12, 9, 6, 3, 15, and 23.

2. Explain the concept

The mean of a set of numbers is calculated by finding the sum of all the values in the set and dividing that sum by the total number of values (the count).

Formula:

Where:

• $\sum x$ = Sum of all the numbers
• $n$ = Total count of the numbers

3. Show the solution

Step 1: Find the sum of the numbers ($\sum x$) Sum = 10 + 8 + 5 + 11 + 12 + 9 + 6 + 3 + 15 + 23

Let's add them systematically:

• 10 + 8 = 18
• 18 + 5 = 23
• 23 + 11 = 34
• 34 + 12 = 46
• 46 + 9 = 55
• 55 + 6 = 61
• 61 + 3 = 64
• 64 + 15 = 79
• 79 + 23 = 102

Total Sum = 102

Step 2: Count the number of values ($n$) Counting the list (10, 8, 5, 11, 12, 9, 6, 3, 15, 23), we see there are exactly 10 numbers. $n = 10$

Step 3: Calculate the mean

4. Identify the answer

Comparing our result to the given options: A. 11.2 B. 10 C. 10.2 D. 11.3

The correct option is C.

5. Tip

When calculating the mean of a long list of numbers, group them into pairs or sets of tens to make the addition easier and reduce the risk of a simple arithmetic error. Always double-check your count ($n$) before dividing, as miscounting the number of items is the most common mistake students make in this topic!