To find the missing piece of data that will result in a mean of 8, given the numbers 7, 12, 3, and 11, follow these steps:
1. Determine the total number of values:
We need to account for the 4 given values plus the missing piece, resulting in a total of 5 values.
2. Calculate the desired total sum:
Since the desired mean is 8, for 5 values, the total sum of these values should be:
[tex]\[
8 \times 5 = 40
\][/tex]
3. Calculate the sum of the given values:
Add the given numbers together:
[tex]\[
7 + 12 + 3 + 11 = 33
\][/tex]
4. Find the missing piece of data:
To achieve the total sum of 40, the missing value must be:
[tex]\[
40 - 33 = 7
\][/tex]
Thus, the missing piece of data must be 7 to achieve a mean of 8.
