The mean number of seven numbers is 112. Two of these numbers have the mean of 107. What is the mean of the remaining five numbers?

Let's break down the problem step by step:

1. The mean of **seven numbers** is given as 112. The formula for the mean is:

   \[
   \text{Mean} = \frac{\text{Sum of all numbers}}{\text{Total number of numbers}}
   \]

   So, the sum of the seven numbers is:

   \[
   \text{Sum of seven numbers} = 112 \times 7 = 784
   \]

2. We are also told that two of these numbers have a mean of 107. Therefore, the sum of these two numbers is:

   \[
   \text{Sum of two numbers} = 107 \times 2 = 214
   \]

3. To find the sum of the remaining five numbers, subtract the sum of the two numbers from the sum of all seven numbers:

   \[
   \text{Sum of remaining five numbers} = 784 - 214 = 570
   \]

4. Finally, the mean of the remaining five numbers is:

   \[
   \text{Mean of five numbers} = \frac{\text{Sum of remaining five numbers}}{5} = \frac{570}{5} = 114
   \]

Thus, the mean of the remaining five numbers is **114**.

Would you like more details or have any questions?

Here are five related questions to expand your understanding:

1. How would the mean change if the sum of the seven numbers increased?
2. If the two numbers had a mean of 105 instead of 107, what would the mean of the remaining five be?
3. What if the total number of numbers was 10, but the mean stayed the same?
4. How does the distribution of numbers around the mean affect the sum?
5. What happens to the overall mean if one of the numbers is changed?

**Tip**: When dealing with means, always remember that the sum of the numbers plays a central role in all calculations!

Solve the problem of finding the mean of five numbers when the mean of seven numbers is 112 and two numbers have a mean of 107. Learn key concepts like arithmetic mean and detailed steps to calculate the solution.

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