Question

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, 102, 102, 102, 103, 103, 108, 127, 127, 129, 129, 141, 159, 164, 164, 164, and 174. Calculate the sample mean and sample standard deviation. Round your answers to 2 decimal places.

Answer 1

Answer:

The sample mean is 127.33 kN and sample standard deviation is 26.59 kN.

Step-by-step explanation:

We are given the following in the question:

97, 97, 102, 102, 102, 103, 103, 108, 127, 127, 129, 129, 141, 159, 164, 164, 164, 174

Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$  

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.  

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{2292}{18} = 127.33$

Sum of squares of differences = 12730

$s = \sqrt{\frac{12730}{17}} = 26.59$

Thus, the sample mean is 127.33 kN and sample standard deviation is 26.59 kN.