Question

Consider the following data:

−3,−2,7,13,−2,−1
Calculate the value of the sample variance. round your answer to one decimal place.

Answer 1

The sample variance of the data set is calculated by squaring the deviations of each data point from the mean, summing these squares, and then dividing by the number of data points minus one. The sample variance rounded to one decimal place is 42.4.

Step-by-step explanation:

To calculate the sample variance for the data set −3, −2, 7, 13, −2, −1, follow these steps:

1. First, find the mean (average) of the numbers. The sum of the data is (−3) + (−2) + 7 + 13 + (−2) + (−1) = 12, and there are six numbers, so the mean is 12 / 6 = 2.
2. Next, calculate the deviation of each number from the mean, then square each deviation.
3. Add the squared deviations: 25 + 16 + 25 + 121 + 16 + 9 = 212.
4. Since this is a sample and not the entire population, divide by n − 1, which is 6 − 1 = 5 (the degrees of freedom).
5. The sample variance is then 212 / 5 = 42.4.