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: ____________

(b) assume the data set {5, 5, 5, 6, 6, 6, 6, 6, 7} gives the ages of a simple random sample of the students in mr. miller’s kindergarten class. 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 population mean (μ)

Sum=5+5+5+6+6+6+6+6+7=52, N=9, μ=52/9≈5.78

Step2: Calculate population standard deviation (σ)

Sum of squared deviations≈3.5586, σ=√(3.5586/9)≈0.63

Step3: Calculate sample mean (x̄)

Sum=52, n=9, x̄=52/9≈5.78

Step4: Calculate sample standard deviation (s)

Sum of squared deviations≈3.5586, s=√(3.5586/8)≈0.67

Answer:

(a)
Mean: Symbol=μ, Value=5.78
Standard deviation: Symbol=σ, Value=0.63
Explain: μ is population mean; σ is population standard deviation.

(b)
Mean: Symbol=x̄, Value=5.78
Standard deviation: Symbol=s, Value=0.67
Explain: x̄ is sample mean; s is sample standard deviation.