The mean of four numbers is 18 . If one of the four numbers is removed, the mean of the
three remaining numbers is 17 . What is the value of the number that was removed?

Question

The mean of four numbers is 18 . If one of the four numbers is removed, the mean of the three remaining numbers is 17 . What is the value of the number that was removed?

UpStudy AI · Accepted Answer

To find the value of the number that was removed, let's break down the problem step by step.

1. **Calculate the Total Sum of the Four Numbers:**
   
   The mean of four numbers is given as 18. The mean is calculated by dividing the total sum of the numbers by the number of numbers. Therefore, the total sum ($$ S_4 $$) of the four numbers is:
   
   $$
   S_4 = \text{Mean} \times \text{Number of items} = 18 \times 4 = 72
   $$

2. **Calculate the Total Sum of the Remaining Three Numbers:**
   
   After removing one number, the mean of the remaining three numbers is 17. Similarly, the total sum ($$ S_3 $$) of these three numbers is:
   
   $$
   S_3 = \text{Mean} \times \text{Number of items} = 17 \times 3 = 51
   $$

3. **Determine the Removed Number:**
   
   The removed number ($$ x $$) can be found by subtracting the sum of the remaining three numbers from the original total sum:
   
   $$
   x = S_4 - S_3 = 72 - 51 = 21
   $$

**Answer:**  
The number that was removed is **21**.
The number removed is 21.

The mean of four numbers is 18 . If one of the four numbers is removed, the mean of the
three remaining numbers is 17 . What is the value of the number that was removed?

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