Question

For a given set of observations for distance measurements, the standard error was computed as \( \pm 2.5 \, {cm} \). Assuming that the observations conform to normal error distribution theory, the probable error will be given by \( \pm \, \underline{{1.5cm}} \, {cm} \) (rounded off to 2 decimal places).

Hint:

To compute the probable error from standard error, multiply by 0.6745—this gives the range within which 50% of normally distributed values lie.

Answer 1

The formula for Probable Error (P.E.) based on Standard Error (S.E.) is given by: \[ {P.E.} = 0.6745 \times {S.E.} \] Given: \[ {S.E.} = 2.5 \, {cm} \] \[ {P.E.} = 0.6745 \times 2.5 = 1.68625 \, {cm} \] Rounding to 2 decimal places: \[ {P.E.} \approx \pm 1.69 \, {cm} \] Hence, the probable error lies between \( \pm 1.67 \, {cm} \) and \( \pm 1.69 \, {cm} \).