In a factory, the time during working hours in which a machine is not operating as a result of breakage or failure is called downtime. The following distribution shows a sample of 100 downtimes of a certain machine( rounded to the nearest minutes):

Downtime

0-9

10-19

20-29

30-39

40-49

50-59

60-69

70-79

80-89

Frequency

3

13

30

25

14

8

4

2

1

With reference to the above distribution, calculate

a) the mean b) standard deviation c) the median d) the quartiles Q1 and Q3 e) the deciles D1 and D9 f) the percentiles P5 and P95

g) person's first and second coefficients of skewness

h) the modal downtime of the distribution by empirical formula ( using the result obtained in part a) and part c) only. Compare this result with the mode obtained in part (g)