Question

Eight measurements were made on the inside diameter of forged piston rings used in an automobile engine. The data (in millimeters) are 74.001, 74.003, 74.015, 74.000, 74.005, 74.002, 74.007, and 74.000. Calculate the sample mean and sample standard deviation. Round your answers to 3 decimal places. Sample mean

Answer 1

Answer: The sample mean and sample standard deviation is 74.004 millimeters and 0.005 millimeters respectively.

Step-by-step explanation:

The given values : 74.001, 74.003, 74.015, 74.000, 74.005, 74.002, 74.007, and 74.000.

$\text{Mean =}\dfrac{\text{Sum of all values}}{\text{Number of values}}\\\\\Rightarrow\overline{x}=\dfrac{ 592.033}{8}=74.004125\approx74.004$

The sample standard deviation is given by :-

$\sigma=\sum\sqrt{\dfrac{(x-\overline{x})^2}{n}}\\\\\Rightarrow\ \sigma=\sqrt{\dfrac{0.000177}{8}}=0.00470372193056\approx0.005$

Hence, the sample mean and sample standard deviation is 74.004 millimeters and 0.005 millimeters respectively.