Standard Deviation for Tram Travel
(2 x 5) + (2.5 x 2) + (3 x 5) + (4 x 4) + (5 x 15) + (6 x 7) + (7 x 4) + (8 x 2) = 207
207 ÷ 44 = 4.704 (Rounded)
Mean / = 4.704
Total of (Xi - )² = 118.6591
Xi Amount = 44
118.6591 ÷ 44 = 2.696797727
Variance = 2.696797727
Standard Deviation = √2.696797727
Standard Deviation = 1.642 (Rounded)
Means of Travel: Combination
Travelling by combination is used mostly between the distance of 3km – 3.99km, but travelling by a combination is used through out all the distances. The lower quartile is 3Km, the median is 3.7Km , the upper quartile is 5.5Km and the inter-quartile range is 2.5Km.
Standard Deviation for Combination Travel
(1x5) + (2 x 3) + (2.5) + (3 x 12) + (4) + (4.5 x 2) + (5 x 6) + (6 x 2) +
(7) + (8.5) = 120
120 ÷ 34 = 3.529 (Rounded)
Mean / = 3.529
Total of (Xi - )² = 107.4706
Xi Amount = 44
107.4706 ÷ 44 = 2.442513636
Standard Deviation = √2.442513636
Variance = 2.442513636
Standard Deviation = 1.563 (Rounded)
Standard Deviation Comparison
The results from the standard deviation show me that travelling by car has the greatest variation in it, and using combinations to travel has the least variation in it.
This means the data for travelling by car is more spread than any other form of travel and the opposite for travelling to school using a combination. Travelling by bike is also high it is about 0.1 below the result for car.
As the standard deviation is the lowest for travelling by using combination it tells me that the data is less spread than any other form of travelling.
Box Plot Comparison
After using cumulative frequency to get my medians, lower quartiles, upper quartiles, and inter-quartile ranges, I was able to create box plots. I can now use the box plots and compare them with each other.
By comparing the median I can tell that walking has the lowest median and travelling by tram has the highest median.
The lower quartile is also the smallest overall for walking and the highest is for the bus.
The upper quartile is again the smallest overall for walking the highest is for tram.
The inter-quartile will be the lowest for walking as it has the least difference between the lower and upper quartiles. The highest inter-quartile range is for bus, but all the inter-quartile ranges are very close, ranging from 2.2Km – 2.9Km apart from walking.
I predicted that the results for walking will be the lowest out of all the types of travel and I was right, this is because a person can only walk a certain distance, not too much, you will not find many people that walk more than about 3-4Km to school.
The median is most closest to the lower quartile for walking than any other travel, the median that is most closest to the higher quartile is for travelling by tram.
Using box plots and comparing them has been very useful for me, this is because it will give me evidence that I have proven my hypothesis.
Outliers
Bike: The outliers will be below 1.25 and above 6.25
Bus: The outliers will be below 2.65 and above 6.05
Car: The outliers will be below 1.1 and above 5.5
Walking: The outliers will be below 0.7 and above 3.5
Tram: The outliers will be below 1.2 and above 6
Combination: The outliers will be below 1.25 and above 6.25
Conclusion
I think my hypothesis has been proven, the reasons are followed below.
First of all my results for walking show me that a person can only live up to a certain distance from school, if they are going to walk. This is because 48 out of the 58 students that walk to school travel less than 3Km.
Someone travelling by bike may only be able to cycle to a certain distance. This is why 15 out of 21 people travel to school by bike below the distance of 3Km.
Travelling by bus can be used by anyone that lives near or far, so travelling by bus is used for nearly all distances, with the frequency not being very high for one amount of distance compared to another. The same is for car.
Travelling by tram is used by nobody that has to travel a distance of 1 – 1.99 Km. This may be because many of people will either walk as it is a small distance to walk, and a small amount may travel by car, bus or bike.
Combination is evenly spread out, this is because people living far may use the bus, car or tram to travel to a certain distance then walk the rest of the way.
My hypothesis, The distance a student lives from the school determines they method of travel they use to get to school, is proven because students living closer to the school walk, as the distance from school increase the means of travel change.