Final answer:
To find the value of k, we need to solve for the population variance using the provided data set. The population variance is given as 18.5.
Step-by-step explanation:
To find the value of k, we need to solve for the population variance using the provided data set. The population variance is given as 18.5.
Population variance = sum of squares of deviations from the mean / total number of data points
Let's assume the data set is represented as {1.2k, 1.6k, 2.3k, 2.9k, 3.1k}.
To calculate the population variance, we first need to find the mean of the data set. The mean is calculated by summing all the data points and dividing by the total number of data points:
Mean (μ) = (1.2k + 1.6k + 2.3k + 2.9k + 3.1k) / 5 = 2.42k
Next, we need to calculate the sum of squares of deviations from the mean:
Sum of squares of deviations = [(1.2k - 2.42k)^2 + (1.6k - 2.42k)^2 + (2.3k - 2.42k)^2 + (2.9k - 2.42k)^2 + (3.1k - 2.42k)^2]
Solving the above equation will give us the sum of squares of deviations. We can then divide this by the total number of data points to calculate the population variance:
Population variance = Sum of squares of deviations / total number of data points
By plugging in the values, we can solve for k.