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

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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. Such a random method would however give no indication of whether the duration of calls remained constant over time. Random sampling may allow a certain cluster of calls to dominate the general trend.

Stratified sampling would not be appropriate for the investigation because we want to find out the number of 5-minute calls, not just select a certain number of them. This sampling method would be useful for a sub-investigation, for example to see how much effect the over 5-minute calls make to the charging by only selecting the over 5-minute calls and assessing their magnitude.

Another way of sampling would be to select every x call, where x is the result of 886/50 rounded down to the nearest whole integer. This would mean recording the call duration for every 17th call (because 886/50 = 17.72). This will generate more that 50 samples, however, 50 is a minimum not a maximum. As the data is probably accurate, there cannot be any outliners.

Please note: a computer maths or spreadsheet package has not been used in the preparation of this report.

Thus, the data collected is given bellow (and then sorted by hand):

Call duration in seconds

Cell duration in seconds (sorted)

53

0

50

1

0

20

20

31

413

33

45

33

274

34

99

35

48

35

50

35

00

35

53

35

54

36

42

36

44

37

1

38

08

38

36

38

38

39

54

41

47

41

41

42

54

42

35

42

47

44

50

45

269

45

42

47

35

47

55

48

35

50

227

50

35

50

33

53

36

53

39

54

70

54

35

54

077

55

38

57

31

99

33

00

45

07

266

08

34

20

07

70

20

227

57

269

38

274

37

413

42

077

41

266

Table 1 - raw data and raw data sorted

Analysis

Mean

A mean gives some idea of central tendency (the average call duration). It will however, be affected by the extreme values '413', '1077' and '1266'. Therefore, it seems appropriate to measure the mean with and without the 3 values.
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With the 3 values (done using a calculator, to 2 d.p.): ==112.56 seconds or 1 minute 52.56 seconds

Clearly, this answer is higher than most of the times, so not particularly representative.

With out the 3 values (done using a calculator, to 2 d.p. ): ==63.2 seconds or 1 minute 3.2 seconds.

The second answer seems more representative, but still does not take account of the majority of the times.

Mode

The mode is another measure of central tendency that gives the most frequent call duration. The mode is clearly 35 seconds (because ...

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