Final answer:
The variance of the remaining 5 observations, after removing the two given ones from the original 7, is calculated to be 21.6, or as a fraction, 112/5.option c is correct
Step-by-step explanation:
The mean (μ) of 7 observations is 8, and variance (σ^2) is 16. Given two observations are 6 and 8, we can find the mean and variance of the remaining 5 observations. The sum of all 7 observations is 7×8 = 56. Subtracting the two given observations, we have a total of 42 for the remaining 5 observations, thus the mean for these 5 observations is 42×5 = 8.4.
To calculate the variance of the 5 observations, we use the formula σ^2 = (Σ(xi - μ)^2)/n, where xi represents the observation values, μ is the mean of these values, and n is the number of observations. Since we know that the variance for all 7 observations is 16, the sum of squared deviations for the 7 observations is 16×7 = 112. We can find the sum of squared deviations for the given observations 6 and 8 from their mean, which is (6-8)^2 + (8-8)^2 = 4. Subtracting this from the total squared deviations we get 112 - 4 = 108. Thus, the sum of squared deviations for the remaining 5 observations is 108, and their variance is 108×5 = 21.6 or 108/5, which as a fraction is 216/10 or 108/5, so the answer is 112/5.