Statistics

The sum of all deviations from the arithmetic mean of the numerical sequence 4, 6, 51, 77, 90, 93, 95, 109, 113, 117 is:

Correct result:

x =  0

Solution:

Σx=755 xˉ=Σx/10=75.5  Δ1=75.5−4=71.5 Δ2=75.5−6=69.5 Δ3=75.5−51=24.5 Δ4=75.5−77=−1.5 Δ5=75.5−90=−14.5 Δ6=75.5−93=−17.5 Δ7=75.5−95=−19.5 Δ8=75.5−109=−33.5 Δ9=75.5−113=−37.5 Δ10=75.5−117=−41.5  x=ΣΔi=0\Sigma x = 755 \ \\ \bar{x} = \Sigma x / 10 = 75.5 \ \\ \ \\ \Delta_{ 1 } = 75.5 - 4 = 71.5 \ \\ \Delta_{ 2 } = 75.5 - 6 = 69.5 \ \\ \Delta_{ 3 } = 75.5 - 51 = 24.5 \ \\ \Delta_{ 4 } = 75.5 - 77 = -1.5 \ \\ \Delta_{ 5 } = 75.5 - 90 = -14.5 \ \\ \Delta_{ 6 } = 75.5 - 93 = -17.5 \ \\ \Delta_{ 7 } = 75.5 - 95 = -19.5 \ \\ \Delta_{ 8 } = 75.5 - 109 = -33.5 \ \\ \Delta_{ 9 } = 75.5 - 113 = -37.5 \ \\ \Delta_{ 10 } = 75.5 - 117 = -41.5 \ \\ \ \\ x = \Sigma \Delta_i = 0

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