Question

Find the population variance and standard deviation. 4,13,25,31,37 Choose the correct answer below. Fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. σ 2 = B. s 2 = hoose the correct answer below. Fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. s= B. σ=

Answer 1

The sample variance (s²) for the data set is 180, and the sample standard deviation (s) is approximately 13.41641.

Step-by-step explanation:

When calculating the population variance (σ²) and standard deviation (σ), it is important to note if the data represents a sample or a population.

The numbers provided by the student, 4, 13, 25, 31, 37, are usually considered as a sample because they are unlikely to represent an entire population. Therefore, we'll calculate the sample variance (s²) and the sample standard deviation (s).

Step 1: Calculate the mean (μ) by adding all numbers and dividing by the count.
μ = (4 + 13 + 25 + 31 + 37) / 5 = 110 / 5 = 22.

Step 2: Determine each value's deviation from the mean, square it, and then calculate the average of those squared deviations to determine the variance.
(4-22)² + (13-22)² + (25-22)² + (31-22)² + (37-22)²
= 324 + 81 + 9 + 81 + 225 = 720
s² = 720 / (5-1) = 720 / 4 = 180.

Step 3: Calculate the sample standard deviation (s) by taking the square root of the sample variance (s²).
s = √180 ≈ 13.41641.