Answer to Question #258465 in Statistics and Probability for Zack

Question

Mzee Kobe Bank wished to establish the times in seconds that each ATM transaction takes. A sample of ATM users were observed and the time in seconds each spent at the ATM was as follows:

Time  (seconds)

10-19

20-29

30-39

40-49

50-59

Number of customer

15

60

67

98

2

 

i. Calculate the coefficent of variation of the waiting time?  ( 6 marks)

Answer 1

coefficent of variation:

$CV=\sigma/\mu$

$\mu=\sum(m_if_i)/N$

where m is midpoint of the class,

f is frequency.

$\mu=\frac{14.5\cdot15+24.5\cdot60+34.5\cdot67+44.5\cdot98+54.5\cdot2}{15+60+67+98+2}=35$

$\sigma=\sqrt{\frac{f_i(m_i-\mu)^2}{N}}=\sqrt{\frac{ 15(14.5-35)^2+60(24.5-35)^2+67(34.5-35)^2+98(44.5-35)^2+2(54.5-35)^2}{242}}=9.65$