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Investigating how much the 5 pence minimum charge on local calls increases the cost of making local calls.

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Introduction

MEI Statistics 1 coursework Investigating how much the 5 pence minimum charge on local calls increases the cost of making local calls. Aim The aim of this coursework is to discover how much the 5 pence minimum charge (to quote BT: 'the minimum charge for each call remains at 5p inclusive of VAT') on local calls increases the cost of making local calls. This information would then be used to ascertain whether moving to a telephone operator without a minimum fee would be a good idea. If moving would save money, then it would be worth doing. Certainly, looking over the current bill, it seems like there are many calls less than 5 minutes (as local rates are 1 pence per minute during the evening and weekend and the phone is always switched off during the daytime). Data Collection The population is the entirety of local calls made during 3-month period. This population is formed because of the procession of only one itemised bill, which happens to be from 1st of November to the 1st of February. The current telephone operator is BT. This bill (i.e. the population) lists 886 calls, with a total duration of 30 hours, 38 minutes and 57 seconds. The complete cost for this period is �50.30 (to the nearest 2 d.p., before VAT). The population is continuous because time can be given to any number of decimal places. The data is surly as accurate as it is possible to be - only untraceable computer bugs could explain inaccuracies. As computer problems are unlikely for a large multi-national firm, such as BT, we can consider the data within the population to be reliable and good quality. A sample method appropriate here could be random sampling. An example of this might be labelling 886 pieces of paper, throwing them into a hat and selecting 50. Also, a computer could be used to select 50 random integer numbers in the range of > 0 and < 887. ...read more.

Middle

38 1444 38 1444 39 1521 41 1681 41 1681 42 1764 42 1764 42 1764 44 1936 45 2025 45 2025 47 2209 47 2209 48 2304 50 2500 50 2500 50 2500 53 2809 53 2809 54 2916 54 2916 54 2916 55 3025 57 3249 99 9801 100 10000 107 11449 108 11664 120 14400 170 28900 227 51529 269 72361 274 75076 413 170569 1077 1159929 1266 1602756 Table 3 - call durations sorted and squared (using a calculator) (calculated using un-rounded values, and checked using the statistical function of the calculator.) Therefore, 2/3rd of the call durations lie within 224.89 seconds. 224.89 seconds is 3 minutes 44.89 seconds, showing that 2/3rd's of the call durations lie within 5 minutes of the mean. This strongly indicates that changing operator would be beneficial. Number of call durations less than 5 minutes Another useful calculation would be to calculate how many of the call durations fall below 5 minutes (300 seconds). If we consider the sample reasonably representative then we can say that the ratio of under 5 minute to over 5 minute calls is 49:3. If the sample is representative, then this means there is a very high number of calls bellow 5 minutes. Displays Box and whisker diagram A good was of summarising some of the calculations above would be a box and whisker diagram. This is figure 1. Frequency polygon A frequency polygon is an appropriate method of discovering the shape of the distribution (see figure 2 and sheet F2). Please note that the last 3 call lengths were not included, as this would have adversely affected the scale and not given a meaningful display. Figure 2 shows a slight positive skew. There is a tight distribution about 20-60 seconds. After 60 seconds, there are occasional calls lengths. Cumulative frequency diagram Suspecting a tight distribution, a cumulative frequency diagram was created (the straighter the 'S' shape, the tighter the distribution about the median). ...read more.

Conclusion

As a change in operator may affect all charge rates, the affect upon the cost of national and international calls should be assessed or else savings from the removal of the 5 pence minimum charge could be negated and the new operator forsaken (and it may in fact cost to return to BT). There are in fact only 5 international calls, totalling 1 hour 4 minutes in duration and costing a total of �12.77. With such a small population, statistical analysis in not advised. Merely cost comparing the call charges with other operators should be sufficient. In addition it should be remarked that the cost for the international calls is quite low and would probably not negate a saving made from removing the 5-minute minimum charge. This is especially true as many non-BT operators are constantly advertising their low international rates. There are 57 national calls, of which total duration is 2 hours and 17 minutes, and costing a total of �5.48. With such a small charge, it hardly seems worth investigating. It would be possible to see how much the same call time (2 hours and 17 minutes) would cost with another operator. It might be advised as a further extension to the investigation, to find out (of the sample data) how many extra minutes are actually charged for because of the 5-minute minimum charge. This would help discover how much one would save when moving to a new operator. In conclusion, it seems that several statements can be made: o The sample is fairly accurate (with the population being as accurate as possible), but could be improved in terms of representation. o The cost of over five minute local calls, national and international calls should be calculated against any increase in charges of another operator to ensure that the increase's effect does not take away the effect of removing the 5 minute minimum charge. o Most local rate calls are less than five minutes in duration, but it is possible that some of the over 5 minute calls are particularly long in duration. ?? ?? ?? ?? Page 1 of 12 ...read more.

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