Final answer:
The mean is 41.3, the median is 39, and the population standard deviation is 17.00.
Step-by-step explanation:
The mean is calculated by summing up all the numbers in the data set and dividing it by the total number of values. In this case, the sum is 413 and there are 10 values, so the mean is 413/10 = 41.3.
To find the median, we first arrange the numbers in ascending order: 12, 19, 27, 31, 35, 43, 51, 53, 62, 64. Since there are 10 values, the median is the average of the 5th and 6th numbers, which is (35 + 43)/2 = 39.
To calculate the population standard deviation, we first find the variance by subtracting the mean from each number, squaring the result, and summing all the squared differences. Then, we divide this sum by the total number of values. The variance is 289.3, so the standard deviation is the square root of the variance, which is 17.00.