Questions: Find the variance for the following data set: 12 22.8 18.2 4.8

Solution Steps

To find the variance of a data set, we need to follow these steps:

1. Calculate the mean (average) of the data set.
2. Subtract the mean from each data point and square the result.
3. Find the average of these squared differences.

First, we calculate the mean (\(\mu\)) of the data set: \[ \mu = \frac{2628162320 + 12 + 22.8 + 18.2 + 4.8}{5} \] \[ \mu = \frac{2628162377.8}{5} \] \[ \mu = 525632475.56 \]

Next, we subtract the mean from each data point and square the result: \[ (2628162320 - 525632475.56)^2 = 4.4263 \times 10^{18} \] \[ (12 - 525632475.56)^2 = 2.7629 \times 10^{17} \] \[ (22.8 - 525632475.56)^2 = 2.7629 \times 10^{17} \] \[ (18.2 - 525632475.56)^2 = 2.7629 \times 10^{17} \] \[ (4.8 - 525632475.56)^2 = 2.7629 \times 10^{17} \]

Finally, we find the average of these squared differences to get the variance (\(\sigma^2\)): \[ \sigma^2 = \frac{4.4263 \times 10^{18} + 2.7629 \times 10^{17} + 2.7629 \times 10^{17} + 2.7629 \times 10^{17} + 2.7629 \times 10^{17}}{5} \] \[ \sigma^2 = \frac{1.1052 \times 10^{19}}{5} \] \[ \sigma^2 = 2.2103 \times 10^{18} \]

Final Answer