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Maths Statistics Coursework - Comparing the relationship Between Gas Cost and Temperature

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Maths Statistics Coursework Comparing the relationship Between Gas Cost and Temperature By James Sanders - June 2001 King Edward VI School Aims I hope to show by my investigation that the winter does mean that the gas bills will be higher than in summer and I hope to be able to aid my grand parents in predicting the costs of the bills for a few more quarters. I hope to show that the bills are very regular which is good and why we have used more gas in some years than others. Also I hope to forecast the next quarterly bills. I want to do this so that my grandparents can have a clear idea of what they should be doing each quarter by cutting down on gas consumption. Prediction I predict that in my examination of the relationship between Gas cost and Temperature I will find that there is an inverse or opposite relationship between them. I also predict that the price of my Gas bills in the future shall be quite similar as my data table has shown but I want to predict that this will carry on. Data Table YEAR MONTH PRICE (�) TEMP (C 1998 M 131.52 6 1998 J 54.41 9.6 1998 S 33.62 15.2 1998 D 85.19 10.6 1999 M 125.68 5.3 1999 J 68.42 9.9 1999 S 26.25 15.9 1999 D 74.78 11.4 2000 M 124.99 5.7 2000 J 71.36 9.2 2000 S 39.27 15.7 2000 D 70.13 10.5 (FIG.1) ...read more.


Standard Deviation = ((x2 - x2 N 54.412+68.422+71.362 = 12733.9941 12733.9941 = 4244.6647 - 4186.09 = 58.5747 3 (58.5747 = 7.653411064 = �7.7 (1.d.p) September Mean = 33.62+26.25+39.27 = 33.046666666 3 = �33.0 (1.d.p) Standard Deviation = ((x2 - x2 N 33.622+26.252+39.272 = 3361.4498 3361.4498 = 1220.4999933 - 1089 = 31.4999933333 3 (31.49999333 = 5.612480141 = �5.6 (1.d.p) December Mean = 85.19+74.78+70.13 = �76.7 (1.d.p) 3 Standard Deviation = ((x2 - x2 N 85.192+74.782+70.132 = 17767.6014 17767.6014 = 5922.5388 - 5882.89 = 39.6438 3 (39.6438 = 6.296332266 = �6.3 (1.d.p) Gas Bill Month Average Standard Deviation M �127.40 �2.78 J �64.70 �7.70 S �33 �5.60 D �76.70 �6.30 The Standard Deviation that I have calculated shows that in the bill for March there is not that much difference between the bills as the standard deviation is �2.78 and that is reflected by the bill prices as well. In the month of June there is a larger difference as the month is a lot more unpredictable than the others are. The months that the bill covers can be either warm or cold and therefore there is a larger difference. In the month of September there is a smaller difference than in June but a larger difference than in March this could be due to the fact that British summers are not regular and are not warm all the time the British summers are generally warm and wet, which allows for a drop in temperature in some of the days. ...read more.


I would also have drawn some of my graphs on computer so they would have been more accurate. Also perhaps I would have used the units of gas used as well and done a cumulative frequency chart and box and whisker plots. Fig.7 shows that there is an inverse relationship between the gas cost and the temperature as when the temperature is low the gas cost is high and vice versa. This also demonstrates as well the fact that March is the most expensive and the coldest time in the year and September is the warmest and the cheapest. I think that is also an accurate way of showing the data as they are all on the same graph and they both are plotted next to each other. This makes it an easy way of showing the gap difference and the relationship that they have. In fig.3 it shows that there is an inverse relationship between Gas cost and temperature, which I predicted earlier as if Gas cost, is high then the temperature should be low which I have proved on my graph. This graph is quite significant as it shows the relationship between the two aspects of Gas I am studying. In fig.4 I have calculated the next quarterly bills that my family should expect to pay. I have plotted these on a graph to show the trend line and how the price deviates off the trend line. ...read more.

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