Question

In: Statistics and Probability

Listed below are costs​ (in dollars) of roundtrip flights between two cities. All flights involve one...

Listed below are costs​ (in dollars) of roundtrip flights between two cities. All flights involve one stop and a​ two-week stay. Find the coefficient of variation for each of the two sets of​ data, then compare the variation.

30 days in advance: 266 292 273 252 278 291 314

One day in advance: 455 615 555 964 615 1050 540

1. The coefficient of variation for the prices of tickets purchased 30 days in advance is %

2. The coefficient of variation for the prices of tickets purchased 1 day in advance is %

3. is there a difference in variation between the two sets?

Solutions

Expert Solution

X: costs​ (in dollars) of roundtrip flights between two cities in 30 days in advance

Y: costs​ (in dollars) of roundtrip flights between two cities in One day in advance

Sr.No. X X-Xbar (X-Xbar)^2
1 266 -14.86 220.82
2 292 11.14 124.10
3 273 -7.86 61.78
4 252 -28.86 832.90
5 278 -2.86 8.18
6 291 10.14 102.82
7 314 33.14 1098.26
Total 1966 2448.86
Xbar = total / 7 280.86 S^2 = total / 7 349.84
S=Sqrt(S^2) 18.70

From above table , n1 = 7 , xbar = 280.86 , S1 = 18.70

Sr.No. Y Y-Ybar (Y-Ybar)^2
1 455 -229.86 52835.62
2 615 -69.86 4880.42
3 555 -129.86 16863.62
4 964 279.14 77919.14
5 615 -69.86 4880.42
6 1050 365.14 133327.2
7 540 -144.86 20984.42
Total 4794 311690.9
Ybar= total / 7 684.86 S2^2 = total / 7 44527.27
S2=Sqrt(S2^2) 211.01

n2 = 7 ; Ybar = 684.86 ; S2 = 211.01

Coefficeint of variation = CV= (Std deviation / mean ) *100

1) The coefficient of variation for the prices of tickets purchased 30 days in advance is?

CV1 = (S1 / xbar ) *100

= ( 18.70 / 280.86) *100

= 0.066 * 100

= 6.66 %

2) The coefficient of variation for the prices of tickets purchased 10 days in advance is?

CV2 = (S2 / ybar ) *100

= ( 211.01/ 684.86) *100

= 0.3081

= 30.81 %

3)

is there a difference in variation between the two sets?

CV1 = 6.66 % < CV2 = 30.81 %

So we can say that the 10 day advance have more variation than the 30 days advance.

More varaiotion in the 10 day advance prices .


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