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Mean: 42

Median: 38

Range: 52

Mean Deviation: 11.23

Shift 1

18

25

56

42

29

38

54

47

35

30

Shift 2

23

19

50

49

67

34

30

59

40

33

Shift 3

19

22

24

40

45

29

33

29

39

59

Shift 4

21

23

25

40

35

19

70

40

22

23

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?

A) Shift 1

B) Shift 2

C) Shift 3

D) Shift 4

Given that the summary of the population is:

Mean: 42

Median: 38

Range: 52

Mean Deviation: 11.23

To obtain the sample that is closest to the mean we shall proceed as follows:

Shift 1:

18,25,56,42,29,38,54,47,35,30

The mean of the sample is:

(18+25+56+42+29+38+54+47+35+30) / 10

=374/10

=37.4

Shift 2:

23, 19, 50, 49, 67,34,30,59,40, 33

The mean is:

(23+19+50+49+67+34+30+59+40+33) / 10

=404/10

=40.4

Shift 3:

Shift 3

19, 22, 24, 40, 45, 29, 33, 29, 39, 59

The mean of the values

(19+22+24+40+45+29+33+29+39+59) / 10

=339/10

=33.9

Shift 4:

21, 23, 25, 40, 35, 19, 70, 40, 22, 23

The mean of the values is:

(21+23+25+40+35+19+70+40+22+23) / 10

=318/10

=31.8

From the calculations, the sample that has mean that is close to population mean is Shift 2