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, 74.006, and 74.000. Calculate the sample mean and sample standard deviation. Round your answers to 3 decimal places. Sample mean = Sample standard deviation =

Answer 1

Solution:

x	x2
74.001	5476.148
74.003	5476.444
74.015	5478.2202
74	5476
74.005	5476.74
74.002	5476.296
74.006	5476.888
74	5476
---	---
x=592.032	x2=43812.7363

The sample mean is

Mean     = (x / n) )

=74.001+74.003+74.015+74+74.005+74.002+74.006+748

=592.032 /8

=74.004

Sample mean =74.004

The sample standard is S

  S =( x² ) - (( x)² / n ) n -1

=(43812.7363-(592.032)²8 )/ 7

=( 43812.7363-43812.7361) /7

=0.0002 /7

=0

= 0.005

Sample standard deviation = 0.005