Final answer:
To calculate the mean, add up all the values and divide by the number of values. The mean of the given sample is 8.2. To calculate the standard deviation, subtract the mean from each value, square the result, add up all the squared values, divide by the number of values minus 1, and take the square root of the result. The standard deviation of the given sample is approximately 0.9166.
Step-by-step explanation:
To calculate the mean of a sample, add up all the values and divide by the number of values. In this case, the sum of the unemployment rates is 7.9 + 7.7 + 9.5 + 7.1 + 8.8 = 41. The number of values is 5. So, the mean is 41 / 5 = 8.2.
To calculate the standard deviation of a sample, subtract the mean from each value, square the result, add up all the squared values, divide by the number of values minus 1, and take the square root of the result. Using the formula:
√((7.9 - 8.2)² + (7.7 - 8.2)² + (9.5 - 8.2)² + (7.1 - 8.2)² + (8.8 - 8.2)²) / (5 - 1) = √(0.09 + 0.25 + 1.44 + 1.21 + 0.36) / 4 = √3.35 / 4 ≈ √0.8375 = 0.9166.