20-2x
20-x
20
20+x
20+2x
What is the average (arithmetic mean) of the list of number above?

Options

A. `20`
B. `100`
C. `20+(x)/(5)`
D. `(100)/(x)`

Answer

To find the average (arithmetic mean) of the given list of numbers, we will follow these steps:

1. **List the Numbers**: The numbers provided are:
- \(20 - 2x\)
- \(20 - x\)
- \(20\)
- \(20 + x\)
- \(20 + 2x\)

2. **Sum the Numbers**: We will add all the numbers together:
\[ (20 - 2x) + (20 - x) + 20 + (20 + x) + (20 + 2x) \]

3. **Combine Like Terms**: Let's simplify the expression by combining like terms:
- The constant terms: \(20 + 20 + 20 + 20 + 20 = 100\)
- The \(x\) terms: \(-2x - x + x + 2x = 0\)

Therefore, the sum of the numbers is:
\[ 100 + 0 = 100 \]

4. **Count the Numbers**: There are a total of 5 numbers in the list.

5. **Calculate the Average**: The average is calculated by dividing the sum of the numbers by the total count of numbers:
\[ \text{Average} = \frac{\text{Sum of Numbers}}{\text{Count of Numbers}} = \frac{100}{5} = 20 \]

Thus, the average (arithmetic mean) of the list of numbers is \(20\).