Question:
The absolute deviations of 8 points from the datum line of a surface are 10, 15, 12, 10, 13, 12, 20 and 25 μm. The root mean square value of the surface roughness (in μm) is \(\underline{\hspace{2cm}}\) (round off to one decimal place).
The absolute deviations of 8 points from the datum line of a surface are 10, 15, 12, 10, 13, 12, 20 and 25 μm. The root mean square value of the surface roughness (in μm) is \(\underline{\hspace{2cm}}\) (round off to one decimal place).
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RMS roughness gives more weight to larger deviations, unlike arithmetic mean roughness.
Updated On: Jan 13, 2026
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Correct Answer: 15 - 16
Solution and Explanation
Given deviations (in μm):
\[
10,\ 15,\ 12,\ 10,\ 13,\ 12,\ 20,\ 25.
\]
RMS value is:
\[
R_q = \sqrt{\frac{1}{n} \sum_{i=1}^n x_i^2}.
\]
Compute squares:
\[
10^2=100,\;
15^2=225,\;
12^2=144,\;
10^2=100,
\]
\[
13^2=169,\;
12^2=144,\;
20^2=400,\;
25^2=625.
\]
Sum:
\[
100+225+144+100+169+144+400+625 = 1907.
\]
Thus:
\[
R_q = \sqrt{\frac{1907}{8}}
= \sqrt{238.375}
= 15.43.
\]
Rounded to one decimal place:
\[
15.4\ \mu m.
\]
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