In: Statistics and Probability
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?
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 .