If the mean of 26, 28, 25, x, 24 is 27, find the value of x

Answer

To find the value of \( x \) in the given problem, we will follow these steps:

### Step 1: Understand the Mean Formula
The mean (average) of a set of numbers is calculated using the formula:
\[ \text{Mean} = \frac{\text{Sum of all observations}}{\text{Number of observations}} \]

### Step 2: Identify the Given Values
We are given the numbers: 26, 28, 25, \( x \), and 24. The mean of these numbers is given as 27.

### Step 3: Count the Number of Observations
In this case, we have 5 observations: 26, 28, 25, \( x \), and 24.

### Step 4: Set Up the Equation
Using the mean formula, we can set up the equation:
\[ 27 = \frac{26 + 28 + 25 + x + 24}{5} \]

### Step 5: Multiply Both Sides by the Number of Observations
To eliminate the fraction, multiply both sides of the equation by 5:
\[ 27 \times 5 = 26 + 28 + 25 + x + 24 \]

### Step 6: Calculate \( 27 \times 5 \)
Calculating the left side:
\[ 27 \times 5 = 135 \]
So, we have:
\[ 135 = 26 + 28 + 25 + x + 24 \]

### Step 7: Calculate the Sum of Known Values
Now, calculate the sum of the known values on the right side:
\[ 26 + 28 + 25 + 24 = 103 \]
Thus, we can rewrite our equation as:
\[ 135 = 103 + x \]

### Step 8: Solve for \( x \)
To find \( x \), subtract 103 from both sides:
\[ x = 135 - 103 \]
Calculating this gives:
\[ x = 32 \]

### Final Answer
The value of \( x \) is \( 32 \).

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