q1 calculate the arithmetic mean using short cut method and step deviation method?

value: frequency

10-20 16

10-30 40

10-40 76

10-50 96

10-60 112

10-70 120

10-80 125

Class Interval
(C.I.)
Frequency
(f)
Mid-point
(m)
Deviation
(d)
fd d fd
10 - 20 16 15 -30 - 480 - 3 48
20 - 30 40 25 -20 - 800 - 2 80
30 - 40 76 35 -10 - 760 - 1 76
40 - 50 96 45 - - - -
50 - 60 112 55 10 1120 1 112
60 - 70 120 65 20 2400 2 240
70 - 80 125 75 30 3750 3 375
   Σf = 585      Σfd = 5230    Σf d'= 523


Short Cut MethodX =A+ ΣfdNX = 45 + 5230585 = 53.94Step Deviaton MethodX =A+ Σfd'N× iX = 45 + 523585× 10 = 53.94

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