Question

Steel Factory Workers Ages

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

Answer 1

The answer is shift 2

Explanation:

Answer 2

Solution: We are given the population mean
`=42`

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:

`Mean=(18+25+56+42+29+38+54+47+35+30)/(10)=(374)/(10)=37.4`

The mean of shift 2 is:

`Mean=(23+19+50+49+67+34+30+59+40+33 )/(10)=(404)/(10)=40.4`

The mean of shift 3 is:

`Mean=(19+22+24+40+45+29+33+29+39+59  )/(10)=(339)/(10)=33.9`

The mean of shift 4 is:

`Mean=(21+23+25+40+35+19+70+40+22+23  )/(10)=(318)/(10)=31.8`

We clearly see the mean of shift 2 is close to the population mean. Hence the option B) Shift 2 is correct.