Math Problem Statement

An article in the Journal of Structural Engineering (Vol. 115, 1989) describes an experiment to test the yield strength of circular tubes with caps welded to the ends. The first yields (in kN) are 97, 97, 103, 103, 104, 104, 108, 125, 125, 128, 128, 140, 159, 160, 160, 168, and 171. Calculate the sample mean and sample standard deviation. Round your answers to 2 decimal places.

Solution

The sample mean is approximately 126.83 kN, and the sample standard deviation is approximately 26.51 kN, both rounded to two decimal places.

Would you like further details or explanations? Here are some related questions to explore:

  1. How is the sample mean calculated from a dataset?
  2. What is the significance of using sample standard deviation instead of population standard deviation?
  3. How do outliers affect the sample mean and standard deviation?
  4. Why do we use n−1n-1 (degrees of freedom) when calculating the sample standard deviation?
  5. How can the standard deviation help in understanding the spread of data?

Tip: Always use n−1n-1 when calculating the sample standard deviation to account for the smaller sample size compared to the population.

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Math Problem Analysis

Mathematical Concepts

Statistics
Sample Mean
Sample Standard Deviation

Formulas

Sample Mean: (sum of data points) / (number of data points)
Sample Standard Deviation: sqrt((Σ(xi - x̄)²) / (n - 1))

Theorems

Empirical Rule
Degrees of Freedom (n-1)

Suitable Grade Level

Grades 10-12

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