Question

The following data are the distances from the workplace (in miles) for the 5 employees of a small business:

15, 14, 17, 16, 18

Assuming that these distances constitute an entire population, find the standard deviation of the population, find the styandard deviation of the population.

Round your answer to at least two decimal places

Answer 1

To find the standard deviation of the employee commute distances, the mean is calculated, the squared differences are summed, divided by the number of data points, and the square root is taken. The population standard deviation is approximately 1.41 miles.

Step-by-step explanation:

The question involves calculating the standard deviation of a population. The distances from the workplace for the 5 employees are given as 15, 14, 17, 16, and 18 miles. Since these distances represent the entire population, we will use the population standard deviation formula:

1. Calculate the mean (average) of the data.
2. Subtract the mean from each data point and square the result.
3. Sum all the squared differences.
4. Divide the sum by the number of data points (N).
5. Take the square root of the value obtained in step 4 to find the standard deviation.

Now, let's do the math:

1. Mean (μ) = (15 + 14 + 17 + 16 + 18) / 5 = 80 / 5 = 16
2. Squared differences: (15-16)², (14-16)², (17-16)², (16-16)², (18-16)²
3. Sum = 1 + 4 + 1 + 0 + 4 = 10
4. Divide by N (which is 5): 10 / 5 = 2
5. Standard deviation (σ) = √2 ≈ 1.41 (rounded to two decimal places)

Therefore, the standard deviation of the population is approximately 1.41 miles.