The mean of 5 observations 1,2,6,x and y is 4.4 and their variance is 8.24 , then x+y is

Options

A. 4
B. 9
C. 15
D. 13

Answer

To solve the problem, we need to find the values of \( x + y \) given that the mean of the observations \( 1, 2, 6, x, y \) is \( 4.4 \) and their variance is \( 8.24 \).

### Step 1: Calculate the Mean
The mean of a set of observations is calculated using the formula:
\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}} \]
For our observations \( 1, 2, 6, x, y \):
\[ \text{Mean} = \frac{1 + 2 + 6 + x + y}{5} = 4.4 \]

### Step 2: Set Up the Equation
Now, we can set up the equation based on the mean:
\[ \frac{1 + 2 + 6 + x + y}{5} = 4.4 \]
Calculating the sum of the known observations:
\[ 1 + 2 + 6 = 9 \]
So the equation becomes:
\[ \frac{9 + x + y}{5} = 4.4 \]

### Step 3: Multiply Both Sides by 5
To eliminate the fraction, multiply both sides by 5:
\[ 9 + x + y = 4.4 \times 5 \]
Calculating \( 4.4 \times 5 \):
\[ 4.4 \times 5 = 22 \]
Thus, we have:
\[ 9 + x + y = 22 \]

### Step 4: Solve for \( x + y \)
Now, we can isolate \( x + y \):
\[ x + y = 22 - 9 \]
Calculating the right side:
\[ x + y = 13 \]

### Final Answer
Thus, the value of \( x + y \) is:
\[ \boxed{13} \]