Question

a group of data items and their mean are given.
360, 405, 455, 460, 480, 600, mean = 460
a. find the deviation from the mean for each of the data items.
b. find the sum of the deviations in part (a).
a. type the deviation from the mean for each of the data items.
360 405 455 460 480 600
(simplify your answers.)
b. the sum of the deviations in part (a) is
(simplify your answer.)

Explanation:

Step1: Calculate deviation for each data item

Deviation formula: \(x_i-\bar{x}\)
For \(x = 360\): \(360 - 460=-100\)
For \(x = 405\): \(405 - 460=-55\)
For \(x = 455\): \(455 - 460=-5\)
For \(x = 460\): \(460 - 460 = 0\)
For \(x = 480\): \(480 - 460=20\)
For \(x = 600\): \(600 - 460 = 140\)

Step2: Calculate sum of deviations

Sum \(=-100+( - 55)+(-5)+0 + 20+140\)
\(=(-100-55 - 5)+(20 + 140)\)
\(=-160+160\)
\(=0\)

Answer:

a. \(-100\), \(-55\), \(-5\), \(0\), \(20\), \(140\)
b. \(0\)