Mayfield High. I have decided to make my hypothesis: The distance a student lives from the school determines they method of travel they use to get to school.

Standard Deviation for Bike Travel

1+1+1+1+1+1.5+1.5+1.5+1.5+2+2+2 +2+2+2.5+3+4+4+8.75+6+6 = 55.25

55.25 ÷ 21 = 2.631 (Rounded) 

Mean or = 2.631

Total of (Xi -  )² = 84.452381

n = 21

84.452381 ÷ 21 = 4.0215 (Rounded)

Variance = 4.0215

Standard Deviation = √4.0215

Standard Deviation = 2.005 (Rounded)

The standard deviation is 2.005, this is how far the data is away from the mean, as it is quite high this tells me that travelling by bike is

Means of Travel: Bus

Travelling by bus is very popular for students that are travelling up to 6.99km to school, for the first 1.99km it was only used by 4 students, but from 2 – 3.99km it was used by a total of 26 students. From 4 – 6.99km travelling by bus was used by another 23 students, from there onwards it starts to decrease. The lower quartile is 2.8Km, the median is 4Km, the upper quartile is 5.7Km and the inter-quartile range is 2.9Km.

Standard Deviation for Bus Travel

(1 x 2) + (1.5 x 2) + ( 2 x 9) + (2.5 x 3) + (3 x 11) + (3.5 x 3) + (4 x 9) +

( 5 x 8) + (6 x 6) + (7 x 4) + (10 x 2) = 234

234 ÷ 59 = 3.966 (Rounded)

Mean / = 3.966

                                        Total of (Xi -  )² = 223.9322

n = 59

223.9322 ÷ 59 = 3.795461017

Variance =   3.795461017

Standard Deviation = √3.795461017

Standard Deviation = 1.948 (Rounded)

Means of Travel: Car

Travelling by car is used by most of the students that travel by car to school and only have to travel 4.99km, this is 40 students. Only 10 more students travel by car, when the distance is 5km and more. The lower quartile is 2.3Km, the median is 2.9Km, the upper quartile is 4.5Km and the inter-quartile range is 2.2Km.

Standard Deviation for Car Travel

(1 x 8) + (1.5) + (1.75 x 2) + ( 2 x 14) + (2.5) ( 3 x 8) + (4 x 6) + (5 x 3) +

(6 x 2) + (7 x 2) + (8) + (8.5) + (10) = 159

159 ÷ 50 = 3.18

Mean or = 3.18

                                                 

Total of (Xi -  )² = 222.225

n = 50

222.225 ÷ 50 = 4.4445

Variance = 4.4445

Standard Deviation = √4.4445

Standard Deviation = 2.108 (Rounded)

The standard deviation shows me …. FINISH THIS BIT OFF

Means of Travel: Walking

48 out of the 58 Students that walk to school, have to walk 2.99km and below. From the distance of 3km the amount of students walking to school decreases, only 10 students walk to school from the distance of 3km to 9.99km. The lower quartile is 1.3km, the median is 1.9Km, the upper quartile is 2.7Km and the inter-quartile range is 1.4Km.

Standard Deviation for Walking

(0.5 x 7) + (1 x 21) + (1.5 x 4) + (2 x 15) + (2.5) + (3 x 3) + (4 x 3) + (6 x 2) + (8) + (9) = 113

113 ÷ 58 = 1.948 (Rounded)

Mean / = 1.948

                                 

                                  Total of (Xi -  )² = 169.5401

Xi Amount = 58

169.5401 ÷ 58 = 2.923105172

Variance = 2.923105172

Standard Deviation = √2.923105172

Standard Deviation = 1.7097 (Rounded)

Means of Travel: Tram

Students that have to travel a distance of 1.99km or less to school do not travel to school using a tram at all. From the distance of 2km the use of tram as travel is used, until 8.99km. The lower quartile is 3.8Km, the median is 5.5Km, the upper quartile is 6.2Km and the inter-quartile range is 2.4Km.

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) 2.108   1.7097 1.642

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 Conclusion

Standard Deviation for:

Bike = 2.005

Bus = 1.948

Car = 2.108  

Walking = 1.7097

Tram = 1.642  

Combination = 1.563

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.