Central Tendency DefinitionCentral Tendency DefinitionDefinition of Measures of Central TendencyA measure of central tendency is a measure that tel s us where the middle of a bunch of data
lies. The three most common measures of central tendency are the mean, the median, and
the mode.
More about Measures of Central TendencyMean: Mean is the most common measure of central tendency. It is simply the sum of the
numbers divided by the number of numbers in a set of data. This is also known as average.
Median: Median is the number present in the middle when the numbers in a set of data are
arranged in ascending or descending order. If the number of numbers in a data set is even,
then the median is the mean of the two middle numbers.
Mode: Mode is the value that occurs most frequently in a set of data.
Examples of Measures of Central TendencyFor the data 1, 2, 3, 4, 5, 5, 6, 7, 8 the measures of central tendency are
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Measure of central tendency is measure of location of the middle (center) of a distibution.
Common measures of measures of central tendency are Mean, Median and Mode.
Compare Dispersion.
Definition The mean, median and mode of a set of data are measures of central tendency,
i.e. they measure where the 'middle' of the data is. Also cal ed centrality.
the range of a given data set is the difference between the largest number and the smal est
number in the data set. For example, in the data set {6, 6, 7, 8, 11, 13, 15}, the range is 15 -
6, which equals 9.
The median is the middle number in the data set when the numbers are written from least to
greatest. So in the data set above, the median is 8. If there is no middle number in the data
set, the median is the average of the two middle numbers. The mode is the number in a data
set that appears most often. So in the data set above, the mode is 6.
Median (Q2): the number that divides the data into two equal halves. The piece of data that is
exactly in the middle, when arranged in numerical order.
Lower Quartile (Q1): the number that divides the lower half of the data into two equal halves.
Upper Quartile (Q3): the number that divides the upper half of the data into two equal halves.
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Poisson Distribution ExamplesPoisson Distribution ExamplesDefinition :In statistics, poisson distribution is one of the discrete probability distribution. This distribution
is used for calculating the possibilities for an event with the given average rate of value(). A
poisson random variable(x) refers to the number of success in a poisson experiment.
Template:Probability distribution In probability theory and statistics, the Poisson distribution is
a discrete probability distribution that expresses the probability of a number of events
occurring in a fixed period of time if these events occur with a known average rate and
independently of the time since the last event.
The Poisson distribution can also be used for the number of events in other specified intervals
such as distance, area or volume. The distribution was discovered by Simeon-Denis Poisson
(1781-1840) and published, together with his probability theory, in 1838 in his work
Recherches sur la probabilite des jugements en matieres criminel es et matiere civile
("Research on the Probability of Judgments in Criminal and Civil Matters").
The work focused on certain random variables N that count, among other things, a number of
discrete occurrences (sometimes called "arrivals") that take place during a time-interval of
given length.
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If the expected number of occurrences in this interval is , then the probability that there are
exactly k occurrences (k being a non-negative integer, k = 0, 1, 2, ...) is equal to
where
e is the base of the natural logarithm (e = 2.71828...)
k is the number of occurrences of an event - the probability of which is given by the function
k! is the factorial of k
is a positive real number, equal to the expected number of occurrences that occur during the
given interval. For instance, if the events occur on average every 4 minutes, and you are
interested in the number of events occurring in a 10 minute interval, you would use as model a
Poisson distribution with = 10/4 = 2.5.
As a function of k, this is the probability mass function. The Poisson distribution can be
derived as a limiting case of the binomial distribution. The Poisson distribution can be applied
to systems with a large number of possible events, each of which is rare. A classic example is
the nuclear decay of atoms. The Poisson distribution is sometimes cal ed a Poissonian,
analogous to the term Gaussian for a Gauss or normal distribution.
The Poisson distribution is appropriate for applications that involve counting the number of
times a random event occurs in a given amount of time, distance, area, etc. Sample
applications that involve Poisson distributions include the number of Geiger counter clicks per
second, the number of people walking into a store in an hour, and the number of flaws per
1000 feet of video tape.
The Poisson distribution is a one-parameter discrete distribution that takes nonnegative
integer values. The parameter, , is both the mean and the variance of the distribution. Thus,
as the size of the numbers in a particular sample of Poisson random numbers gets larger, so
does the variability of the numbers.
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