This statistics problem is solved step by step below, with detailed explanations to help you understand the method and arrive at the correct answer.
ScanSolve AI Answer
The population standard deviation of the given data set is 2. Steps to calculate the population standard deviation: 1. Calculate the mean (μ): μ = (2 + 4 + 4 + 4 + 5 + 5 + 7 + 9) / 8 μ = 40 / 8 μ = 5 2. Calculate the variance (σ²): For each data point (x), subtract the mean (μ) and square the result (x - μ)². Then sum these squared differences and divide by the total number of data points (N). (2 - 5)² = (-3)² = 9 (4 - 5)² = (-1)² = 1 (4 - 5)² = (-1)² = 1 (4 - 5)² = (-1)² = 1 (5 - 5)² = (0)² = 0 (5 - 5)² = (0)² = 0 (7 - 5)² = (2)² = 4 (9 - 5)² = (4)² = 16 Sum of squared differences = 9 + 1 + 1 + 1 + 0 + 0 + 4 + 16 = 32 Variance (σ²) = Sum of squared differences / N σ² = 32 / 8 σ² = 4 3. Calculate the standard deviation (σ): The population standard deviation is the square root of the variance. σ = √σ² σ = √4 σ = 2