QUESTION 18 - 1 POINT
The following data set represents the ages of all six grandchildren in a family.
Find the variance for this data set of ages:
$6,3,14,11,14,6$
- Round the final answer to one decimal place.
Provide your answer below:
variance $=\frac{1}{L}$
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Step 1 ：First, we need to calculate the mean of the data set. The mean is calculated by adding all the data points and dividing by the number of data points. In this case, the data points are the ages: 6, 3, 14, 11, 14, 6. The mean is \(\mu = \frac{6+3+14+11+14+6}{6} = 9.0\).

Step 2 ：Next, we subtract the mean from each data point to get the differences: \(6-9 = -3, 3-9 = -6, 14-9 = 5, 11-9 = 2, 14-9 = 5, 6-9 = -3\).

Step 3 ：We then square each of these differences to get: \((-3)^2 = 9, (-6)^2 = 36, 5^2 = 25, 2^2 = 4, 5^2 = 25, (-3)^2 = 9\).

Step 4 ：Finally, we calculate the variance by taking the average of these squared differences. The variance is \(\sigma^2 = \frac{9+36+25+4+25+9}{6} = 18.0\).

Step 5 ：Final Answer: The variance for this data set of ages is \(\boxed{18.0}\).