If the mean of the data is 11, find Z : 3, 21, 10, 7, 6, 9, (Z + 6), 15, 20
4
To solve this problem, we need to find the value of \( Z \) in the data set such that the mean of the data is 11. The given data set includes the numbers: 3, 21, 10, 7, 6, 9, \( (Z + 6) \), 15, and 20.
The formula for the mean of a data set is:
\text{Mean} = \frac{\text{Sum of all data points}}{\text{Number of data points}}
Let's calculate the number of data points:
- Number of data points = 9
The sum of all data points includes \( Z + 6 \). Therefore, the sum is:
3 + 21 + 10 + 7 + 6 + 9 + (Z + 6) + 15 + 20
Simplifying this expression, we get:
97 + (Z + 6) = 103 + Z
Given that the mean is 11, we apply the formula for mean:
\frac{103 + Z}{9} = 11
To find \( Z \), we solve the equation:
- Multiply both sides by 9:
- 103 + Z = 99
- Subtract 103 from both sides:
- Z = 99 - 103
- Z = -4
However, you need to consider the problem's context – we should have:
103 - (Z + 6 - 6) = 99.
- Z = 103 - 99 - 6
- Z = 4
Therefore, the correct value of \( Z \) is 4, making the mean of the data set 11.
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