If the mean of distribution 10,8,15 ,12, K , 25 is 12 , find the value of K.

Options

A. 2
B. 1
C. 4
D. 3

Answer

To find the value of K in the distribution 10, 8, 15, 12, K, 25, given that the mean is 12, we can follow these steps:

### Step 1: Understand the formula for mean
The mean (average) of a set of numbers is calculated by dividing the sum of all the numbers by the total count of numbers.

### Step 2: Set up the equation
We know the mean is given as 12, and we have 6 observations (10, 8, 15, 12, K, 25). Therefore, we can set up the equation:

\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}} \]

Substituting the known values into the equation gives us:

\[ 12 = \frac{10 + 8 + 15 + 12 + K + 25}{6} \]

### Step 3: Calculate the sum of known observations
Now, let's calculate the sum of the known observations:

\[ 10 + 8 + 15 + 12 + 25 = 70 \]

### Step 4: Substitute the sum back into the equation
Now, we can substitute the sum back into the equation:

\[ 12 = \frac{70 + K}{6} \]

### Step 5: Multiply both sides by 6 to eliminate the fraction
To eliminate the fraction, multiply both sides by 6:

\[ 12 \times 6 = 70 + K \]

This simplifies to:

\[ 72 = 70 + K \]

### Step 6: Solve for K
Now, isolate K by subtracting 70 from both sides:

\[ K = 72 - 70 \]

This gives us:

\[ K = 2 \]

### Conclusion
The value of K is 2.

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