Math Problem Statement
Calculate the standard deviation for the following sample sets of data.
41, 41, 38, 27, 53, 56, 28, 45, 47, 49, 55, 60
Note: Round your answer to the nearest tenth.
Solution
as np
Sample data
data = [41, 41, 38, 27, 53, 56, 28, 45, 47, 49, 55, 60]
Calculate standard deviation (sample)
std_dev = np.std(data, ddof=1) # ddof=1 for sample standard deviation
Round to the nearest tenth
std_dev_rounded = round(std_dev, 1) std_dev_roundedThe standard deviation of the given sample data set is 10.5.
Would you like a detailed explanation of how this was calculated or have any other questions?
Here are five related questions for further exploration:
- How do you calculate variance and standard deviation manually?
- What is the difference between sample and population standard deviation?
- How does standard deviation help in understanding data spread?
- Can you calculate the mean of this data set?
- How does changing one data point affect the standard deviation?
Tip: Always verify whether you need a sample or population standard deviation before calculating, as the formulas differ slightly.
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Math Problem Analysis
Mathematical Concepts
Statistics
Standard Deviation
Data Analysis
Formulas
Standard Deviation (Sample) = sqrt((Σ(xi - mean)^2) / (n - 1))
Mean = Σxi / n
Theorems
Concept of Sample Standard Deviation
Suitable Grade Level
Grades 9-12
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