Question

Compute the range and sample standard deviation for strength of the concrete (in psi).3910, 4130, 3500, 3200, 2960, 3820, 4130, 4060

Answer 1

The range is the difference between the maximum and minimum value.

The maximum value is 4130 and the minimum is 2960. The range is then: 4130-2960=

A standard deviation of the sample is calculated with this formula:

$s=\sqrt{\frac{1}{n-1}\sum ^n_{i=1}(x_i-M)^2}$

where n is the sample size, xi is each of the values of the sample and M is the mean of the sample.

First, we have to calculate the mean.

This is done as:

$\begin{gathered} M=\frac{1}{n}\sum x_i=\frac{1}{8}(3910+4130+3500+3200+2960+3820+4130+4060) \\ M=\frac{1}{8}\cdot29710 \\ M=3713.75 \end{gathered}$

Now, we can start calculating the standard deviation.