## Posts Tagged 'Statistics'

### The Improbability Principle

Extremely improbable events are commonplace.

It’s an unusual day if nothing unusual happens”. This aphorism encapsulates a characteristic pattern of events called the Improbability Principle. Popularised by statistician Sir David Hand, emeritus professor at Imperial College London, it codifies the paradoxical idea that extremely improbable events happen frequently.  [TM112 or search for “thatsmaths” at irishtimes.com].

From front cover of  The Improbability Principle

### The Citizens’ Assembly: Why do 10 Counties have no Members?

Recently, the Irish Government established the Citizens’ Assembly, a body of 99 citizens that will consider a number of constitutional issues. The Assembly meets on Saturday to continue its deliberations on the Eighth Amendment to the Constitution, which concerns the ban on abortion. It will report to the Oireachtas (Parliament) on this issue in June [TM106 or search for “thatsmaths” at irishtimes.com].

### Twenty Heads in Succession: How Long will we Wait?

If three flips of a coin produce three heads, there is no surprise. But if 20 successive heads show up, you should be suspicious: the chances of this are less than one in a a million, so it is more likely than not that the coin is unbalanced.

### Mathematics Solving Crimes

What use is maths? Why should we learn it? A forensic scientist could answer that virtually all the mathematics we learn at school is used to solve crimes. Forensic science considers physical evidence relating to criminal activity and practitioners need competence in mathematics as well as in the physical, chemical and biological sciences [TM080: search for “thatsmaths” at irishtimes.com ].

Trigonometry, the measurement of triangles, is used in the analysis of blood spatter. The shape indicates the direction from which the blood has come. The most probable scenario resulting in blood spatter on walls and floor can be reconstructed using trigonometric analysis. Such analysis can also determine whether the blood originated from a single source or from multiple sources.

This week, That’s Maths in The Irish Times ( TM044 ) is about the originator of Students t-distribution.

In October 2012 a plaque was unveiled at St Patrick’s National School, Blackrock, to commemorate William Sealy Gosset, who had lived nearby for 22 years. Sir Ronald Fisher, a giant among statisticians, called Gosset “The Faraday of Statistics”, recognising his ability to grasp general principles and apply them to problems of practical significance.

Plaque at St Patrick’s National School, Hollypark, Blackrock, where William Gosset lived from 1913 to 1935.

### Population Projections

The Population Division of the United Nations marked 31 October 2011 as the “Day of Seven Billion”. While that was a publicity gambit, world population is now above this figure and climbing. The global ecosystem is seriously stressed, and climate change is greatly aggravated by the expanding population. Accurate estimates of growth are essential for assessing our future well-being. This week, That’s Maths in The Irish Times ( TM034  ) is about population growth over this century. Continue reading ‘Population Projections’

### A Simple Growth Function

Three Styles of Growth

Early models of population growth represented the number of people as an exponential function of time,

$\displaystyle N(t) = N_0 \exp(t/\tau)$

where ${\tau}$ is the e-folding time. For every period of length ${\tau}$, the population increases by a factor ${e\approx 2.7}$. Exponential growth was assumed by Thomas Malthus (1798), and he predicted that the population would exhaust the food supply within a half-century. Continue reading ‘A Simple Growth Function’