STATISTICS AND SERIAL KILLER

One of the aim of statistics is to find pattern in the web of data.
There was a serial killer in Uk by name herald shipman. He was arrested in 1998. He killed at least 215 and 45 escaped. He used his position of authority as a doctor to murder many of his elderly patients. His Modus operandi was to inject his patients with a lethal dose of morphine and then alter their medical records to make their deaths look natural.
The million dollar question is, ' could we have detected shipman's murders earlier?"
The statistics entered. People analysed deaths in shipman's area from 1977. All death certificates were scrutinized. They came to the following conclusions.

1. Shipman's practice record shows much higher number of deaths than average for his area.
2. Time of death of of patients of other doctors were distributed through out the day. but shipman's victims tended to die between 01.00 pm and 5.00 p.m- precisely when shipman undertook his home visits.
3. If someone has been monitoring the data, shipman's activities could have been discovered as early as 1984-15 years earlier-which could have saved up to 175 lives.

Hence statistics can even save hundreds of lives.
When a man applies for a job, the organization asks to furnish all the marks and grades from school level to university level. The organization looks for consistency in the grades. If there is sudden spike in the grades, there may be fraud and the certificates may be fake.
In a competitive examination; in a particular examination center, many candidates scored top level marks and got selected. A fraud was detected later.
If a man spend lavishly all of a sudden, suspicion will arise.
Charts and figures will clearly indicate the abnormality in the data. Trend and pattern clearly predict final outcome. Statistics predict the outcome of election using exit poll results.
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LISSAJOUS FIGURES

Definition: "When a particle is subjected to two sine wave motion or two oscillatory motion at right angles, the particle describes lissajous figures". We know sine wave motion and circular motion is basically same. Hence we draw two circles A and B perpendicular to each other. The circle B rotates twice faster than circle A. That is, frequency of circle B is two times than that of A. A particle at the intersection of two circles is subjected to two sine wave motion A and B at 90 degree simultaneously. The particle will describe figures depending on the frequency and phase of A and B . In our case, the ratio of frequency is 1:2 and the two waves are in phase. To draw lissajous figures : A moving point in both the circles are chosen. Here we should remember; during the time taken by the circle A to complete one rotation, circle B completes two. Hence the points are marked on the circles according to their speed. Then straight lines

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Let us find out how the casino survives with mathematics. Say, your friend invite you for a game of dice. You must bet (wager) 2 dollars. If you roll 'six' you will get back 8 dollars. The game will go on for 30 rounds. All sounds good. The probability of rolling 'six' is 1/6. Since the game will be played for 30 times, the 'expected win' is 30*1/6 = 5. That is, you are expected to win 5 rounds out of 30. Hence your gain will be 5 * 8 =40 dollars. ok. This also implies that you will loose 25 rounds. Hence your loss will be 25*2 =50 dollars. Your net gain will be gain-less = 40-50 = -10 dollars. For 30 rounds, the loss is -10 dollars, Hence, for one round =-10/30 = -1/3 dollars. There will be a loss of -1/3 or 0.33 dollars per round. It is not a fair game. Let us make a simple formula to calculate 'Pay out per round\. The probability for a win = p The pay-out in case of win = V No. of rounds = n The expect

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