Question

[1] Find the combined standard deviation.

SHIFTS 1 2

No. Of

workers

60 40

means 25 20

variance 25 9​

Answer 1

Step-by-step explanation:

Mean of 1&2: X12 = ( (n1X1+ n2X2) / (n1+n2) )

X12 = ( (60*25 + 40*29) / (60+40) )

X12 = 51.11

d1 = X12 - X1 = 51.11 - 25 = 26.11

d2 = X12 - X2 = 51.11 - 20 = 31.11

Combined S.D:

σ12 = ✓( (n1(σ1^2+d1^2) + n2(σ2^2+d2^2)) / (n1+n2) )

= ✓( (60(5^2+26.11^2) + 40(3^2+31.11^2)) / (60+40) )

σ12 = 28.544