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Description: Weighted Mean is an average computed by giving different weights to some of the individual values. If all the weights are equal, then the weighted mean is the same as the arithmetic mean. Whereas weighted means generally behave in a similar approach to arithmetic means, they do have a few counter instinctive properties. Data elements with a high weight contribute more to the weighted mean than do elements with a low weight. The weights cannot be negative. Some may be zero, but not all of them; since division by zero is not allowed. Weighted means play an important role in the systems of data analysis, weighted differential and integral calculus.

Formula:

x=w1x1+ w2x2+….+ wnxnw1 + w2 + ……+ wn

Example:  Enter the Weights to the X values = 5,20,40,80,100

Weighted mean= (W1X1+W2X2+W3X3+…WnXn) / (W1+W2+W3+…Wn)

Weighted mean=(5+40+120+320+500)/(5+20+40+80+100)

Weighted mean=(985)/(245)

Weighted mean=4.020408163265306

Weighted mean(rounded)=4.0204

Description:Root Mean Square is a statistical measure of the effective magnitude for a varying set of values, also called as RMS or Quadratic Mean. The square root of an arithmetic mean of the squares of each exact values of a data set offers RMS value of a data set. RMS is an abbreviation of Root mean square value and also known as Quadratic Mean.

Formula: xrms= x12 + x22 +…….+xn2n

Example: Enter Inputs : 5,20,40,80,100

: 5

xrms = (5)2+ (20)2 + (40)2 + (80)2) + (100)2 5

xrms = 25 + 400 + 1600 + 6400  +10000 5

xrms = 3685

Root Mean Square: 60.7042

Description: The word mean, which is a homonym for multiple other words in the English language, is similarly ambiguous even in the area of mathematics. Depending on the context, whether mathematical or statistical, the mean can be mean because it can mean many different things. In its simplest mathematical definition regarding data sets, the mean used is the arithmetic mean, also referred to as mathematical expectation, or average. In this form, the mean refers to an intermediate value between a discrete set of numbers, namely, the sum of all values in the data set, divided by the total number of values.

Formula: 1) Mean Formula ,

x= 1Ni=1Nxi

2) Median Formula,

Median = (n2)th Term + (n2+1)th Term2

Example:1) Mean Example

Mean = 10 + 2 + 38 + 23 +38 + 23 + 217= 1557= 22.143

2) Median Example

The median is the middle value, so to rewrite the list in order:

13, 13, 13, 13, 14, 14, 16, 18, 21

There are nine numbers in the list, so the middle one will be

9 + 12= 102= 5

5th number, So the median is 1

Description:To estimate the probability of number of success or failure in a sequence of n independent trials or experiments. The success or failure experiment which is used in this calculator is also called as Bernoulli’s experiment or distribution or trial and is the fundamental for the binomial test of statistical significance. In probability & statistics for data analysis, binomial distribution is a discrete probability function widely used method to model the number of successes and failures in n independent numbers of trials or experiments. P(x) is the probability of x successes occur in the n number of events, p is the probability of success and q is the probability of failure often denoted by q = (1 – p).

Formula:

q = 1 – p

Pn(x) = c(n,x)px qn-x

= n!x! (n-x)!px qn-x

Example:

n(Number of Events) = 3,

X(Number of Success) = 1

probability, p = 0.2

Pn(x)= 3!1! (3-1)!(0.2)1(1-0.2)(3-1)

= 61(2)(0.2)(0.8)2

= 3(0.2)(0.64)

Binomial Distribution = 0.384

A permutation is an arrangement of all or part of a set of objects, with regard to the order of the arrangement.

For example, suppose we have a set of three letters: A, B, and C. We might ask how many ways we can arrange 2 letters from that set. Each possible arrangement would be an example of a permutation. The complete list of possible permutations would be: AB, AC, BA, BC, CA, and CB.

When statisticians refer to permutations, they use a specific terminology. They describe permutations as n distinct objects taken r at a time. Translation: n refers to the number of objects from which the permutation is formed; and r refers to the number of objects used to form the permutation. Consider the example from the previous paragraph. The permutations were formed from 3 letters (A, B, and C), so n = 3; and each permutation consisted of 2 letters, so r = 2.

Formula

P(n,r) = n!/(n-r)!

Example

P(12,3) = 12! / (12-3)! = 1,320 Possible Outcomes

The Combinations Calculator will find the number of possible combinations that can be obtained by taking a sample of items from a larger set. Basically, it shows how many different possible subsets can be made from the larger set. For this calculator, the order of the items chosen in the subset does not matter.

Combination is the number of ways, in which you can choose r elements out of a set containing n distinct objects (that’s why such problems are often called “n choose r” problems). The order of choosing the elements is not important.

Formula

C(n,r) = n!/(r! * (n-r)!)

• C is the number of combinations,
• n is the total number of elements in the set,
• r is the number of elements you choose from this set.

Example

C (6,2)= 6!/(2! * (6-2)!)

= 6!/(2! * 4!)

= 15 Possible Combinations

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