The mean of 9 numbers is 10. If one more number is added, the mean remains as 10. Find the number which is added.

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Understand the given information
We know that the mean of 9 numbers is 10.

### Step 2: Calculate the sum of the 9 numbers
The formula for the mean is:
\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}} \]
Given that the mean is 10 and the number of observations is 9, we can rearrange the formula to find the sum:
\[ \text{Sum} = \text{Mean} \times \text{Number of observations} \]
Substituting the values:
\[ \text{Sum} = 10 \times 9 = 90 \]
So, the sum of the 9 numbers is 90.

### Step 3: Add one more number
Now, we add one more number to these 9 numbers. This means the total number of observations will now be 10.

### Step 4: Calculate the new sum with the additional number
It is given that the mean remains 10 even after adding the new number. So, we can calculate the new sum:
\[ \text{New Sum} = \text{Mean} \times \text{New Number of observations} \]
Substituting the values:
\[ \text{New Sum} = 10 \times 10 = 100 \]
So, the new sum of the 10 numbers is 100.

### Step 5: Find the added number
To find the number that was added, we subtract the original sum from the new sum:
\[ \text{Added Number} = \text{New Sum} - \text{Original Sum} \]
Substituting the values:
\[ \text{Added Number} = 100 - 90 = 10 \]

### Conclusion
The number that was added is **10**.

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