**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

**Description:** STP Calculator is an online tool for calculating Standard Temperature and Pressure easily. It takes the inputs and calculates the Standard Temperature and Pressure, so it is handy for solving problems requiring Standard Temperature and Pressure Calculations.

**Formula: **STP = Volume of gas x273TxP760

**Example: **Given parameters are,

Volume of the gas = 0.5L,

T = 300K,

P = 700 Torr

STP = Volume of gas x 273Tx P760

STP = 0.5 x 0.91 x 0.9210

STP = 0.4190L