Find the missing number if the average of all the eight number is 472.
623,164,529,425,___,205,301,824

Options

A. 737
B. 711
C. 723
D. 705

Explanation

To find the missing number in the given set of numbers where the average is known, we can follow these steps:

### Step 1: Understand the average formula
The average of a set of numbers is calculated by dividing the sum of all the numbers by the total count of the numbers. In this case, we have 8 numbers.

### Step 2: Set up the equation
Let the missing number be \( x \). The average of the eight numbers is given as 472. Therefore, we can set up the equation:

\[ \frac{623 + 164 + 529 + 425 + x + 205 + 301 + 824}{8} = 472 \]

### Step 3: Multiply both sides by 8
To eliminate the fraction, multiply both sides of the equation by 8:

\[ 623 + 164 + 529 + 425 + x + 205 + 301 + 824 = 472 \times 8 \]

### Step 4: Calculate \( 472 \times 8 \)
Now, calculate the right side:

\[ 472 \times 8 = 3776 \]

### Step 5: Sum the known numbers
Next, we need to sum all the known numbers on the left side:

\[ 623 + 164 + 529 + 425 + 205 + 301 + 824 \]

Calculating this step by step:

- \( 623 + 164 = 787 \)
- \( 787 + 529 = 1316 \)
- \( 1316 + 425 = 1741 \)
- \( 1741 + 205 = 1946 \)
- \( 1946 + 301 = 2247 \)
- \( 2247 + 824 = 3071 \)

So, the sum of the known numbers is \( 3071 \).

### Step 6: Substitute back into the equation
Now we can substitute this sum back into our equation:

\[ 3071 + x = 3776 \]

### Step 7: Solve for \( x \)
To find \( x \), subtract 3071 from both sides:

\[ x = 3776 - 3071 \]

Calculating this gives:

\[ x = 705 \]

### Conclusion
The missing number is \( 705 \).

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