Question

1. read the directions carefully and answer each part. round to two decimals. (a) assume the data set {5, 5, 5, 6, 6, 6, 6, 6, 7} gives the ages of all mrs. miller’s grandchildren. compute the mean and standard deviation for this set. label each with the appropriate symbol. explain the symbols.

	symbol	value
standard deviation

explain ____

Explanation:

Step1: Calculate sum of data

Sum = 5 + 5 + 6 + 6 + 6 + 6 + 6 + 7 = 47

Step2: Compute mean (μ)

μ = 47 / 8 = 5.875 ≈ 5.88

Step3: Calculate squared deviations

(-0.875)² + (-0.875)² + 5*(0.125)² + (1.125)² = 2.875

Step4: Compute variance (σ²)

σ² = 2.875 / 8 = 0.359375

Step5: Compute standard deviation (σ)

σ = √0.359375 ≈ 0.60

μ is the population mean (average age of all grandchildren), σ is the population standard deviation (measure of age spread).

Answer:

Metric	Symbol	Value
Standard deviation	σ	0.60