Thursday, March 15, 2012

Part: 1 Statistics (Central tendency, Arithmetic mean, Geometric mean,Harmonic mean, )

Central tendency: 
When we are working with a set of data, a common question that comes up is "what is the typical value of the observations made?" In other words, we are trying to find out the 'center' or 'middle' or 'representative' or 'the most typical'  value of a set of data. These are all attempts to identify the central tendency of the data set. There are several different measures of central tendency. ?These are collectively called 'statistical averages'.

An average of a set of values of a variable is a single number, which is 'typical ' of the whole set. The purpose of an average is to represent the distribution and also to afford a basis of comparison with other distributions of similar nature.

Among the several averages the most commonly used averages are--
--Mean (Average)

The means can be of 3 types:
--Arithmetic Mean
--Geometric Mean
--Harmonic Mean
*If not mentioned, the word 'average' means 'arithmetic mean'.

Arithmetic mean: The arithmetic mean is calculated by adding all the observations and dividing this total by the number of observations. Three students have the following marks: 70, 80, 60
:. Arithmetic Mean (A.M) = (70+80+60)/3
                                        = 210/3
                                        =  70
Geometric Mean: The geometric mean, G of n Positive values X1, X2, ...............Xn in defined as the n-th positive root of the product of the values.
Symbolically, G= (X1, X2, ...............Xn) 1/n

Geometric mean of 50x60 = ( 50x60) 1/2
                                         = √50x60
                                         =  54.77
"       "          "    506070    =  (50x60x70) 1/2
                                         =  350x60x70
                                         =  59.44

Harmonic mean : The harmonic mean for a series of n values X1, X2, ...............Xn is defined as
Harmonic Mean, H = n/{(1/X1)+(1/X2)+...(1/Xn)}
In general, the harmonic mean is used when rates are expressed as 'X' per 'Y' and 'X' is constant; such as miles per hours, income per household, production per acre etc. If 'Y' is constant, the arithmetic mean is used.
Note: Whenever total distance is fixed or constant and we have to find out average speed, we will use harmonic mean to find out average.

Example: Suppose, the distance between Dhaka & Narayongonj is 18 km. You drive a car for the first 6 km at a speed 30 km/hr, the second 6 km at a rate of 40 km/hr and the remaining 6 km at a speed of 6 km at a speed of 20 km/ hr. What is your average speed?

Central tendency
In statistics, the term central tendency relates to the way in which quantitative data tend to cluster around some value. A measure of central tendency is any of a .Central Tendency: Introduces the mean, median, and mode.
A guide to the mean, median and mode and which of these measures of central tendency you should use for different types of variable and with skewed ...
Measures of central tendency are measures of the location of the middle or the center of a distribution. The definition of "middle" or "center" is purposely left ...
This lesson describes measures of central tendency, such as the mean, median, mode, proportion, and percentage. From Stat Trek's free, online statistics ...
For a complete lesson on central tendency, or mean median mode range,
To obtain a better understanding of what is considered normal, other measures of central tendency such as the median, the trimmed mean, and the trimean may
The best way to reduce a set of data and still retain its information is to summarize it with a single value.
What will happen to the measures of central tendency if we add the same amount to all data values, or multiply each data value by the same amount?
A measure of central tendency is a measure that tells us where the middle of a bunch of data lies. The three most common measures of central tendency are the ..

Arithmetic mean,
In mathematics and statistics, the arithmetic mean, or simply the mean or average when the context is clear, is the central tendency of a collection of numbers ..
The arithmetic mean of a set of data is presented by Math Goodies. Learn mean at your own pace.
Arithmetic Mean - Definition of Arithmetic Mean on Investopedia - A mathematical representation of the typical value of a series of numbers, computed as the
An arithmetic mean is a fancy term for what most people call an "average." When ... says the average of 10 and 20 is 15, they are referring to the arithmetic mean.
The arithmetic mean of a set of values is the quantity commonly called "the" ... the underlying distribution (known as the population mean), the arithmetic mean of ...
Arithmetic Mean. The most commonly used type of average. To find the arithmetic mean of a set of n numbers, add the numbers in the set and ...
Arithmetic and geometric means, Arithmetic-Geometric Means inequality. General case.
The arithmetic mean is what is commonly called the average of the numbers. The value of $A.M.$ is always between the least and the greatest .
The Arithmetic Mean Calculator is probably the easiest way to learn how to calculate arithmetic mean online because all you have to do is simply enter in a set of ...
geometric mean or means and arithmetic mean how to calculate arithmetic mean center frequency bandwidth calculation average of numbers center frequency .

The geometric mean, in mathematics, is a type of mean or average, which indicates the central tendency or typical value of a set of numbers. A geometric mean
Practical information on how to calculate 'Geometric Means', including its use for shellfish bed and swimming beach classifications and closures.
Geometric Mean - Definition of Geometric Mean on Investopedia - The average of a set of products, the calculation of which is commonly used to determine the ...
and so on. The geometric mean of a list of numbers may be computed using GeometricMean[list] in the ... the geometric mean is related to the arithmetic mean A ...
Free geometric mean calculations online. Find the geometric average mean value of the given numbers. Can be used for calculating or creating new math ...
the geometric mean is relevant any time several quantities multiply together to produce a product. The geometric mean .
Similar right triangles formed by dropping an altitude--explained using an interactive applet, a you tube video and many step by step example problems.
A kind of average. To find the geometric mean of a set of n numbers, multiply the numbers and then take the nth root of the product.
Math lesson covering the geometric mean, from its basic formula and definition to example problems. Learn how to calculate the geometric mean of a set of ...

Harmonic mean
In mathematics, the harmonic mean (sometimes called the subcontrary mean) is one of several kinds of average. Typically, it is appropriate for situations when ...
The harmonic mean of a list of numbers may be computed in Mathematica using HarmonicMean[list]. The special cases of n=2 and n=3 are therefore given by ..
Arithmetic and Harmonic Means. A fellow travels from city A to city B. For the first hour, he drove at the constant speed of 20 miles per hour. Then he ...
Free Harmonic mean calculations online. Find the Harmonics mean of the given numbers. Can be used for calculating or creating new math statistics problems.
John Schuyler project risk and economic decision analysis tip of the week.
To find the harmonic mean of a set of n numbers, add the reciprocals of the numbers in the set, divide the sum by n, then take the reciprocal of ...
Like arithmetic mean and geometric mean, harmonic mean is also useful mean and can be defined as Harmonic mean is quotient of number of the given values ...
Many courses offered by the School of Computer Science and Engineering use a harmonic mean formula to calculate students' final results given their exam ...
The Harmonic Mean. If three numbers are such that by whatever part of itself the largest term exceeds the middle term, and the middle term exceeds the third by ...

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