Mean of 10 numbers is 6. It was later observed that one number was misread as 9. When the correct means was 7, then the correct value of that number is

Options

A. 19
B. 20
C. 8
D. 10

Answer

To solve the problem step by step, let's break it down:

### Step 1: Calculate the Incorrect Sum of the Numbers
The mean of 10 numbers is given as 6. The sum of these 10 numbers can be calculated using the formula:
\[ \text{Sum} = \text{Mean} \times \text{Number of Terms} \]
Substituting the values:
\[ \text{Sum} = 6 \times 10 = 60 \]

**Hint:** Remember that the sum of numbers can be found by multiplying the mean by the total number of terms.

### Step 2: Adjust for the Misread Number
One number was misread as 9. To find the sum of the numbers excluding this misread number, we subtract 9 from the incorrect sum:
\[ \text{Correct Sum (excluding misread number)} = 60 - 9 = 51 \]

**Hint:** When correcting for a misread number, subtract the misread value from the total sum.

### Step 3: Set Up the Equation for the Correct Mean
Let the correct value of the misread number be \( x \). The new sum of the numbers, including the correct number, will be:
\[ \text{New Sum} = 51 + x \]
The mean of the numbers is now given as 7. We can set up the equation:
\[ \frac{51 + x}{10} = 7 \]

**Hint:** The mean is calculated by dividing the total sum by the number of terms.

### Step 4: Solve for the Correct Number
To eliminate the fraction, multiply both sides of the equation by 10:
\[ 51 + x = 70 \]
Now, isolate \( x \):
\[ x = 70 - 51 = 19 \]

**Hint:** To isolate a variable, perform inverse operations (in this case, subtracting 51 from both sides).

### Conclusion
The correct value of the misread number is \( x = 19 \).

**Final Answer:** The correct value of that number is **19**.