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 answer:

x =  0

Step-by-step explanation:

$$\begin{gathered} \mathrm{\Sigma }x=755 \\ \bar{x}=\mathrm{\Sigma }x\mathrm{/}10=75.5 \\ {\mathrm{\Delta }}_1=75.5-4=71.5 \\ {\mathrm{\Delta }}_2=75.5-6=69.5 \\ {\mathrm{\Delta }}_3=75.5-51=24.5 \\ {\mathrm{\Delta }}_4=75.5-77=-1.5 \\ {\mathrm{\Delta }}_5=75.5-90=-14.5 \\ {\mathrm{\Delta }}_6=75.5-93=-17.5 \\ {\mathrm{\Delta }}_7=75.5-95=-19.5 \\ {\mathrm{\Delta }}_8=75.5-109=-33.5 \\ {\mathrm{\Delta }}_9=75.5-113=-37.5 \\ {\mathrm{\Delta }}_{10}=75.5-117=-41.5 \\ x=\mathrm{\Sigma }{\mathrm{\Delta }}_i=0 \end{gathered}$$

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