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Problem 1

Compute the (sample) variance and standard deviation of the given data sample. (You calculated the means in the Section 8.3 exercises. Round all answers to two decimal places.) -1,5,5,7,14

Expert verified
Mean = $$\frac{30}{5}$$ = 6 #tag_title# Step 2: Calculate the squared deviations from the mean. #tag_content# Subtract the mean from each data point and square the result. (-1 - 6)^2 = 49 (5 - 6)^2 = 1 (5 - 6)^2 = 1 (7 - 6)^2 = 1 (14 - 6)^2 = 64 #tag_title# Step 3: Calculate the sample variance. #tag_content# Add the squared deviations and divide by (n - 1), where n is the number of data points. Variance = $$\frac{(49 + 1 + 1 + 1 + 64)}{(5 - 1)}$$ Variance = $$\frac{116}{4}$$ = 29 #tag_title# Step 4: Calculate the sample standard deviation. #tag_content# The standard deviation is the square root of the variance. Standard Deviation = $$\sqrt{29}$$ ≈ 5.39 #Completed_solution# Sample variance = 29, and sample standard deviation ≈ 5.39 (rounded to two decimal places).
See the step by step solution

Step 1: Calculate the mean of the dataset.

Mean is the average value of the dataset. Add all the data points and divide by the number of data points in the dataset. Given data points: -1, 5, 5, 7, and 14. Mean = $$\frac{(-1 + 5 + 5 + 7 + 14)}{5}$$

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