Final answer:
To calculate the variance for the sample data (7, 7, 2, 5, 1), the sample mean is 4.4. Squaring the deviations from the mean and summing them gives 31.2. Dividing by one less than the number of data points results in a sample variance of 7.8.
Step-by-step explanation:
To find the variance for the given sample data (7, 7, 2, 5, 1), follow these steps:
- Calculate the sample mean by adding all the numbers and dividing by the count of the numbers. (7+7+2+5+1)/5 = 22/5 = 4.4.
- Subtract the sample mean from each of the data points and square the result for each: (7-4.4)^2, (7-4.4)^2, (2-4.4)^2, (5-4.4)^2, (1-4.4)^2.
- Calculate the squared differences: 6.76, 6.76, 5.76, 0.36, 11.56.
- Sum the squared differences: 6.76 + 6.76 + 5.76 + 0.36 + 11.56 = 31.2.
- Since this is a sample and not a population, divide by the number of data points minus one (degrees of freedom): 31.2 / (5-1) = 31.2 / 4 = 7.8.
Therefore, the sample variance is 7.8.