A maintenance manager has recorded the time taken by maintenance staff to repair a particular type of equipment fault. The following table shows the time taken in minutes to repair 250 recent faults.
Time taken (minutes)
Frequency
Under 10
28
10 and under 20
54
20 and under 30
81
30 and under 40
57
40 and under 50
23
50 and under 60
7
60 and over
0
(a) Calculate the mean and standard deviation of the time taken
(b) Calculate the coefficient of variation.
Answers
Given : time taken by maintenance staff to repair a particular type of equipment fault.
time taken in minutes to repair 250 recent faults.
To Find :(a) Calculate the mean and standard deviation of the time taken
(b) Calculate the coefficient of variation.
Solution:
Class f Mean Class d=( mean - 25)/10 df
0 - 10 28 5 -2 -56
10 - 20 54 15 -1 -54
20-30 81 25 0 0
30 - 40 57 35 1 57
40 - 50 23 45 2 46
50 - 60 7 55 3 21
250 14
Mean = 25 + 10 x (14)/250
= 25.56
Mean of class intervals² 5², 15² , 25² , 35² , 45² , 55² ,
Frequency 28 , 54 , 81 , 57 , 23 , 7
∑ f *(class interval Mean)² = 201050
Standard deviation² = Variance = ∑ f *(class interval Mean)² /n - (mean)²
= 201050 /250 - (45)²
= 804.2 - 653.3136
= 150.8864
Standard deviation = √150.8864 = 12.2836
Coefficient of Variation = (SD/Mean) * 100 %
(12.2836/25.56) * 100 = 48.06 %
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