Question

3. Southeast Express is a regional, overnight, freight service. Customers can leave their parcels for shipping at drop-off bins. Unfortunately, the bins at often the target of vandals. The losses range from cleaning up graffiti (200) having to replace a destroyed bin ($2,500). The recorded losses last year were: NUMBER OF LOSSES: 10 8 1 LOSS SIZE: $200 $600 $1,000 $2,000 $2,500 2 a. What were the mean (average) and median dollar losses last year? (1.5 points) (note: use (n-1) in b. What is the standard deviation of these historical losses? the denominator when calculating the variance) (2 points)

Answer 1

Answer:

Mean = 604.55

Median = 600

Standard Deviation = 1368.35

Solution:

Calculation of Mean

S.No.	Loss Size (X)	No. of Losses (f)	f*X
1	200	10	2000
2	600	8	4800
3	1000	2	2000
4	2000	1	2000
5	2500	1	2500
	SUM	22	13300

Mean = Sum(f*X)/Sum(f) = 13300/22 = 604.55

Calculation of Median:

S.No.	Loss Size (X)	No. of Losses (f)	Cumulative Frequency (cf)
1	200	10	10
2	600	8	18
3	1000	2	20
4	2000	1	21
5	2500	1	22

N is 22. Average of N/2 and N/2+1 is average of 11 and 12th value. From the CF values in the above table we can see that both the 11th and12th value lies in the category of loss size of 600.

Therefore 600 is the median.

Calculation of Standard Deviation:

Standard Deviation = [Sum {f*(X-Mean)^2}/N-1]^0.5

S.No.	Loss Size (X)	No. of Losses (f)	X- Mean	(X-Mean)^2	f*(X-Mean)^2
1	200	10	-404.55	163660.7025	1636607.025
2	600	8	-4.55	20.7025	165.62
3	1000	2	395.45	156380.7025	312761.405
4	2000	1	1395.45	1947280.703	1947280.703
5	2500	1	1895.45	3592730.703	3592730.703
Sum					7489545.455
Variance					1872386.364
Standard Deviation					1368.35