Answer
a. Mean = $120, sum of variation = 0
b. range = 114, variance = 1467.4286, standard deviation = 38.3070
Work Step by Step
a. Mean = $ ( 89 + 170 + 104 + 113+ 56+ 161+ 147) / 7 = $120
Sum of variation =
(89-120) +(170-120)+(104-120)+(113-120)+(56-120)+(161-120)+(147-120) = 0
b. Range = Largest Value - Smallest Value = 170-56= 114
Variance=
$[(89-120)^{2}+(170-120)^{2}+(104-120)^{2}+(113-120)^{2}+(56-120)^{2}+(161-120)^{2}+(147-120)^{2}] / 7 = (-31)^{2} + 50^{2} + (-16)^{2}+ (-7)^{2}+ (-64)^{2}+ 41^{2} + 27^{2}] / 7 = 10,272 / 7 = 1467.4286$
Standard Deviation =$ \sqrt 1467.4286 = 38.3070$
