18. The mean of the observations $$ 25,17, x, 28,12,8 $$ is 17.5 then find $$ x $$.

Question

UpStudy AI · Accepted Answer

To find the value of $$ x $$ in the dataset $$ 25, 17, x, 28, 12, 8 $$ with a mean of 17.5, follow these steps:

1. **Understand the Mean Formula:**

The mean (average) of a set of numbers is calculated by adding all the numbers together and then dividing by the count of numbers.

$$
   \text{Mean} = \frac{\text{Sum of all observations}}{\text{Number of observations}}
   $$

2. **Set Up the Equation:**

Given that the mean is 17.5 and there are 6 observations, the equation becomes:

$$
   \frac{25 + 17 + x + 28 + 12 + 8}{6} = 17.5
   $$

3. **Calculate the Sum of Known Observations:**

$$
   25 + 17 + 28 + 12 + 8 = 90
   $$

4. **Plug the Sum Back into the Equation:**

$$
   \frac{90 + x}{6} = 17.5
   $$

5. **Solve for $$ x $$:**

Multiply both sides by 6 to eliminate the denominator:

$$
   90 + x = 17.5 \times 6
   $$
   
   $$
   90 + x = 105
   $$
   
   Subtract 90 from both sides:

$$
   x = 105 - 90
   $$
   
   $$
   x = 15
   $$

**Answer:** The value of $$ x $$ is **15**.
$$ x = 15 $$

18. The mean of the observations \( 25,17, x, 28,12,8 \) is 17.5 then find \( x \).