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).

Hint:

RMS roughness gives more weight to larger deviations, unlike arithmetic mean roughness.

Answer 1

Correct Answer: 15 - 16

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: \[ 15.4\ \mu m. \]