Question

If the probability of committing an error follows normal distribution,compute the probable error from the following data:
4.8,4.2,5.1,3.8,4.4,4.7,4.1 and 4.5

Answer 1

Given data is 4.8,4.2,5.1,3.8,4.4,4.7,4.1 and 4.5

Probable error = 50% of the normal distribution times the standard deviation

Probable error = 0.675 * Standard deviation.

Standard Deviation = SD = √(∑(xi-mean)^2/N)

Mean of the above data = (4.8+ 4.2 + 5.1 + 3.8 + 4.4 + 4.7 + 4.1 + 4.5)/8 = 4.45

SD = √( (4.8-4.45)² ) + (4.2-4.4.5)² + (5.1-4.45)²+ (3.8-4.45)²+ (4.4- 4.45)² + (4.7 - 4.45)² + (4.1 - 4.45)² + (4.5 - 4.45)²)/8

(Note that square root is for complete data)

SD = 0.3905

Probable Error = 0.675 * 0.39 = 0.26325