Final answer:
To find the population variance, calculate the mean, square the differences between each value and the mean, sum them up, and divide by the number of values. The population standard deviation is the square root of the variance.
Step-by-step explanation:
To find the population variance, we need to calculate the mean of the data set first. The mean is calculated by summing up all the values and dividing by the number of values: mean = (5 + 11 + 19 + 23 + 27) / 5 = 17. Then, for each value, subtract the mean and square the result. Sum up all these squared differences. Finally, divide this sum by the number of values to get the population variance. In this case, the population variance is ((5-17)^2 + (11-17)^2 + (19-17)^2 + (23-17)^2 + (27-17)^2) / 5 = 82.
The population standard deviation is the square root of the variance. So, the population standard deviation is sqrt(82) ≈ 9.05.