Steel Factory Workers AgesMean: 42 Median: 38 Range: 52 Mean Deviation: 11.23Shift 118255642293854473530Shift 223195049673430594033Shift 319222440452933293959Shift 421232540351970402223The 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?A) Shift 1 B) Shift 2 C) Shift 3 D) Shift 4

Solution: We are given the population mean [tex]=42[/tex]Now, in order to find which shift's mean is closest to population mean, we will find the mean of each shift.The mean of shift 1 is:[tex]Mean=\frac{18+25+56+42+29+38+54+47+35+30}{10}=\frac{374}{10}=37.4[/tex]The mean of shift 2 is: [tex]Mean=\frac{23+19+50+49+67+34+30+59+40+33 }{10}=\frac{404}{10}=40.4[/tex]The mean of shift 3 is: [tex]Mean=\frac{19+22+24+40+45+29+33+29+39+59  }{10}=\frac{339}{10}=33.9[/tex]The mean of shift 4 is: [tex]Mean=\frac{21+23+25+40+35+19+70+40+22+23  }{10}=\frac{318}{10}=31.8[/tex]We clearly see the mean of shift 2 is close to the population mean. Hence the option B) Shift 2 is correct.