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The surface finish of a piece of steel is measured by a number called the Rz. Th

ID: 3204332 • Letter: T

Question

The surface finish of a piece of steel is measured by a number called the Rz. The lower the number, the smoother the surface of the steel. On a parts conveyor line, the hardness of individual pieces was tested. The parts were randomly selected. The Rockwell Hardness is assumed to be normally distributed. The measured values obtained were: 0.90, 0.85, 0.68, 0.75, 0.53, 0.80, 0.85, 0.81, 0.92 A) Find the mean of the above values B) Find the median of the above values C) Find the standard deviation of the above values D) What is the Range of the Values? E) What is the "Statistical Range" (Mean +/-3 Std Deviations)?

Explanation / Answer

a) Mean = sum of all number / total number of value

= 7.09 / 9

= 0.787

b) Median

Arrange all numbers from ascending to descending order

0.53 0.68 0.75 0.8 0.81 0.85 0.85 0.9 0.92

Median is middle value of the number = 0.81

c) Standard deviation

= sqrt[( 0.53 - 0.78) ^2+ ( 0.68 - 0.78) ^2 + ( 0.75 - 0.78) ^2 + ( 0.8 - 0.78) ^2 + ( 0.81 - 0.78) ^2 + ( 0.85 - 0.78) ^2 +(0.85 - 0.78) ^2 + (0.9 - 0.78) ^2 + ( 0.92 - 0.78) ^2 / 9]

= 0.114

d) Range

Smallest value = 0.68 , largest value = 0.92

Range = Largest value - Smallest value

= 0.92 - 0.68

= 0.24

e) Statistical range

Mean + / - 3 * std. deviation

= 0.78 + / - 3 * 0.114

= (0.438 , 1.122)

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