Manuals/calci/HYPGEOMDIST

HYPGEOMDIST(n1,n2,n3,n4)

• $n1$ is the sample's success.
• $n2$ is the sample's size.
• $n3$ is population's success
• $n4$ is the population size.

Description

"This function gives the result of Hypergeometric distribution. This distribution is a discrete probability distribution which is contrast to the binomial distribution. A hypergeometric random variable is the number of successes that result from a hypergeometric experiment. The probability distribution of a hypergeometric random variable is called a hypergeometric distribution. In HYPGEOMDIST(n1,n2,n3,n4) where n1 is thenumber of items in the Sample that are classified as successes. n2 is the total number of items in the sample. n3 is thenumber of items in the population that are classified as successes and n4 is the total number of items in the sample. The following conditions are applied to the Hypergeometric distribution: 1.This distribution is applies to sampling without replacement from a finite population whose elements can be classified into two categories like success or Failure. 2.The population or set to be sampled consists of N individuals, objects,or elements 3.Each individual can be success (S) or a failure (F), and there areM successes in the population. 4. A sample of n individuals is selected without replacement in such a way that each subset of size n is equally likely to be chosen. The Hyper geometric probability distribution is: P(X=x)=h(x;n,M,N)=(M (N-M

                                    x)           n-x)         /(N     
                                                                      n)  for x is an integer satisfying   max(0, n-N+M)<=x<=min(n,M). where x is sample's success.n is the sample's size.M is population's success and N is the population size. Here we can give any positive real numbers. Suppose we are assigning any decimals numbers it will change in to Integers. This function will give result as error when 1. Any one of the argument is nonnumeric.

2.n1<0 or n1 is greater than the smaller value of n2 or n3. 3.n1 is less than the bigger of 0 or(n2-n4+n3) 4. n2<=0 or n2>n4 5.n3<=0 or n3>n4 or n4<=0"

Examples

Draw 6 cards from a deck without replacement. What is the probability of getting two hearts? Here M = 13 number of hearts N = 52 total number of cards so N-M= 52-13= 39 and x=2,n=6 so n-x=6-2=4 HYPGEOMDIST(2,6,13,52)=0.315129882 2.42 balls are numbered 1 - 42. You select six numbers between 1 and 42. What is the probability that they contain (i)match 3? (ii) match 4? (i)Here M= 6,N=42,x=3and n=6 HYPGEOMDIST(3,6,6,42)=0.02722185 (ii)Here M= 6,N=42,x=4and n=6 HYPGEOMDIST(4,6,6,42)=0.001801446 3.

See Also

• BINOMDIST
• COMBIN
• FACT

References

Correlation

(ar1,ar2)

• $ar1$ and $ar2$ are the set of values.

Description

• This function gives the correlation coefficient of the 1st set($ar1$) of values and 2nd set($ar2$) of values.
• Correlation is a statistical technique which shows the relation of strongly paired variables.
• For example, test average and study time are related; those who spending more time to study will get high marks and Average will go down for those who spend less time for studies.
• There are different correlation techniques to measure the Degree of Correlation.
• The most common of these is the Pearson Correlation Coefficient denoted by $r_{x}y$.
• The main result of a correlation is called the Correlation Coefficient($r$)which ranges from -1 to +1.
• The $r$ value is positive i.e +1 when the two set values increase together then it is the perfect Positive Correlation.
• The $r$ value is negative i.e. (-1) when one value decreases as the other increases then it is called Negative Correlation.
• Suppose the $r$ value is 0 then there is no correlation (the values don't seem linked at all).
• If we have a series of $n$ measurements of $X$ and $Y$ written as $xi$ and $yi$ where $i=1,2,...n$ then the Sample Correlation Coefficient is:

$CORREL(X,Y)=r_{xy}={\frac {\sum _{i=1}^{n}(xi-{\bar {x}})(yi-{\bar {y}})}{\sqrt {\sum _{i=1}^{n}(xi-{\bar {x}})^{2}\sum {i=1}^{n}(yi-{\bar {y}})^{2}}}}$

• ${\bar {x}}$ and ${\bar {y}}$ are the sample means of $X$ and $Y$.
• This function will give the result as error when

1.$ar1$ and $ar2$ are non-numeric or different number of data points.
2.$ar1$ or $ar2$ is empty
3.The denominator value is zero.

• Suppose $ar1$ and $ar2$ contains any text, logical values, or empty cells, like that values are ignored.

Examples

1. Find the correlation coefficients for X and Y values are given below :X={1,2,3,4,5}; Y={11,22,34,43,56}

=CORREL(A4:A8,B4:B8)=0.99890610723867

1. The following table gives the math scores and times taken to run 100 m for 10 friends:SCORE(X)={52,25,35,90,76,40}; TIME TAKEN(Y)={11.3,12.9,11.9,10.2,11.1,12.5}

=CORREL(A5:A10,B5:B10)= -0.93626409417769

1. Find the correlation coefficients for X and Y values are given below :X={-4,11,34,87};Y={9,2,59,24}

=CORREL(A1:A4,B1:B4)=0.353184665607273

See Also

• COVAR
• FISHER

References

Correlation