Final answer:
To calculate the sample variance, find the mean of the data, subtract the mean from each data point and square the result, find the sum of all the squared differences, and divide the sum by the number of data points minus one.
Step-by-step explanation:
To calculate the sample variance, we need to follow these steps:
- Find the mean of the data.
- Subtract the mean from each data point and square the result.
- Find the sum of all the squared differences.
- Divide the sum by the number of data points minus one.
In this case, the given data is {-5, -13, 7, -5, 7, 7, -5}. The mean is -0.8571. Subtracting the mean from each data point and squaring the result gives the squared differences: {16.0816, 143.2249, 58.4082, 0.0816, 58.4082, 58.4082, 0.0816}. The sum of the squared differences is 334.6943. Dividing this sum by the number of data points minus one (7-1=6) gives the sample variance: 55.7824. Rounding to one decimal place, the value of the sample variance is 55.8.