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:

  1. How do you calculate variance and standard deviation manually?
  2. What is the difference between sample and population standard deviation?
  3. How does standard deviation help in understanding data spread?
  4. Can you calculate the mean of this data set?
  5. 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