The summary statistics for all of the workers at a steel factory are shown. Four sample groups were taken from each of the four shifts. For which sample group is the mean closest to the population mean?

Mean Shift 1 = (18+25+56+42+29+38+54+47+35+30) / 10
Mean Shift 1 = (364) / 10
Mean Shift 1 =36.4
Absolute value (Mean Shift 1 - Population Mean)
Absolute value (36.4-42)
Absolute value (-5.6) = 5.6

Mean Shift 2 = (23+19+50+49+67+34+30+59+40+33) / 10
Mean Shift 2 = (404) / 10
Mean Shift 2 =40.4
Absolute value (Mean Shift 2 - Population Mean)
Absolute value (40.4-42)
Absolute value (-1.6) = 1.6

Mean Shift 3 = (19+22+24+40+45+29+33+29+39+59) / 10
Mean Shift 3 = (339) / 10
Mean Shift 3 =33.9
Absolute value (Mean Shift 3 - Population Mean)
Absolute value (33.9-42)
Absolute value (-8.1) = 8.1

Mean Shift 4 = (21+23+25+40+35+19+70+40+22+23) / 10
Mean Shift 4 = (318) / 10
Mean Shift 4 =31.8
Absolute value (Mean Shift 4 - Population Mean)
Absolute value (31.8-42)
Absolute value (-10.2) = 10.6

Answer: For sample group 2 (Shift 2) is the mean closest to the population mean.