Question

Consider the following data:

15, −15, 0, 15, −15, 0
Calculate the value of the sample variance.

Answer 1

To calculate the sample variance of the data set 15, -15, 0, 15, -15, 0, one must find the mean, calculate each data point's deviation from the mean, square those deviations, and divide the sum of squared deviations by one less than the number of data points. The calculated sample variance for this data set is 180.

Step-by-step explanation:

The student has provided numerical data and is seeking to calculate the sample variance. Sample variance is a statistical measure that represents the spread of a set of numbers. To calculate the sample variance of the provided data set: 15, -15, 0, 15, -15, 0, we follow these steps:

1. Calculate the sample mean by adding all the data values together and dividing by the number of data points.
2. Subtract the sample mean from each data point to determine the deviation of each point from the mean.
3. Square each deviation to get the squared deviations.
4. Add all the squared deviations together to get the sum of squared deviations.
5. Divide the sum of squared deviations by one less than the number of data points (n - 1) to get the sample variance.

Applying these steps:

1. The sample mean is (15 - 15 + 0 + 15 - 15 + 0) / 6 = 0.
2. The deviations are 15, -15, 0, 15, -15, 0.
3. The squared deviations are 225, 225, 0, 225, 225, 0.
4. The sum of squared deviations is 225 + 225 + 0 + 225 + 225 + 0 = 900.
5. The sample variance is 900 / (6 - 1) = 900 / 5 = 180.

Therefore, the sample variance of the data set is 180.