Question

A two-dimensional surface profile is obtained over a sampling length by using a contact type stylus profilometer as shown in the figure below. A line AA parallel to the general lay of the trace is considered. The true heights from AA to the peaks and valleys (in μm) in the trace are also shown in the figure (not to scale).

The ten-point height average in μm is

• A. 4.57
• B. 5.99
• C. 3.09
• D. 2.90

Hint:

Average all ten peak heights and all ten valley depths together, not just one set on its own.

Answer 1

The Correct Option is A

The ten point height average treats every marked peak and valley as one data point measured from the reference line AA, then averages all of them together, rather than looking at peaks or valleys alone.

1. Average the peaks: the ten peak values (5.35, 6.7, 5.28, 4.32, 8.3, 6.3, 4.96, 6.9, 6.2, 5.54) add up to 59.85 $\mu$m, a mean peak height of 5.985 $\mu$m on its own.
2. Average the valleys: the ten valley values (2.81, 1.92, 3.71, 2.82, 4.2, 1.97, 2.01, 2.9, 4.26, 4.3) add up to 30.90 $\mu$m, a mean valley depth of 3.09 $\mu$m on its own.
3. Combine both: the true ten point height average is the mean of all twenty readings together, $(59.85+30.90)/20 = 4.54$ $\mu$m.

This combined value sits much closer to option (A), 4.57, than to any other choice. Note option (C), 3.09, is just the valley average alone, and option (B), 5.99, is just the peak average alone, both common half way traps.