January 13th, 2008 . by Vanaja
If an event can happen in exactly m ways, and if following it, a second event can happen in exactly n ways, then the two events in succession can happen in exactly mn ways.

Illustration.

Suppose there are five routs from A to B and three routs from B to C. In how many ways a person can go from A to C?

Since there are five different routs from A to b, the person can go the first part of his journey in 5 different ways. Having completed in any one of the 5 different ways , he has 3 different ways to complete the second part of the journey fro B to C. Thus each way of going from A to B give rise to 3 different ways of going from B to C.

There fore the total number of ways of completing the whole journey = number of ways for the first part x number of ways for the second part.

= 5 x 3=15.

Generalisation

If an event can occur in m different ways, a second event in n different ways, a third event in exactly p different ways and so on, then the total number of ways in which all events can occur in succession is mnp….

Posted in Arithmetic, Definitions ** | **
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January 10th, 2008 . by Vanaja
One of the most important objectives of statistical analysis is to get one single value that describes the characteristic of the entire mass of unwieldy data. Such a value is called central value or an average or the expected value of the variable.

The term ” average ” has been defined by various authors. Some important definitions are given below.

- “Average is an attempt to find one single figure to describe whole of figures” -Clark

- ” An average is a single value selected from a group of values to represent them in some way-a value which is supposed to stand for whole group, of which it is a part, as typical of all the values in he group” -A.E Waugh

- ” An average is a typical value in the sense that it is sometimes employed to represent all the individual values in a series or of a variable” -Ya-Lun-Chou

- “An average is a single value within the range of the data that is used to represent all the values in the series.Since an average is somewhere within the range of the data. It is also called a measure of central value” - Croxton &Cowden

Posted in Definitions, Statistics ** | **
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January 6th, 2008 . by Vanaja
I had been busy with some personal matters for the last five six weeks. In between gone for a vacation as well. But the new year day was a bit dull as my kids and I was not well after coming back from the vacation.

I wish you all a very prosperous and happy new year.

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