Arithmatic Mean

-->

The arithmetic mean, often referred to as simply the mean or average when the context is clear, is a method to derive the central tendency of a sample space . The term "arithmetic mean" is preferred in mathematics and statistics because it helps distinguish it from other averages such as the geometric and harmonic mean.

Mean, median, and mode are three kinds of "averages". Arithmetic mean is commonly called as average.Mean or Average is defined as the sum of all the given elements divided by the total number of elements.

Mean formula is

Mean = sum of elements / number of elements

In the next section we shall talk about Mean, Median, Mode and range in detail.

Define Volume

-->

Define Volume: Volume can be defined as” the magnitude or intensity of a certain sound”.

Volume is how much three-dimensional space a substance (solid, liquid, gas, or plasma) or shape occupies or contains,often quantified numerically using the SI derived unit, the cubic metre.Volumes of some simple shapes, such as regular, straight-edged, and circular shapes can be easily calculated using arithmetic formulas. The density of an object is defined as mass per unit volume.

Formula for volume of a cylinder

V = πr²h

Let us now solve one problem to understand the above concept.

Example 1) Find the volume of a cylinder with radius 5 cm and height 10cm.

V = πr²h

V = 3.14*25*10

V = 785cms

AREA OF A QUADRILATERAL

-->

Today let us know on how to find the area of Quadrilateral.

A Quadrilateral is a polygon with four sides. The parts of a quadrilateral are its sides, its four angles, and its two Diagonals. The perimeter of a quadrilateral is the sum of the lengths of its sides.

The area of the quadrilateral can be found by dividing it into triangles and summing the areas of the triangles.

Let us know see some examples on how to calculate the area of a quadrilateral.

Example 1) Calculate the area of a rectangle with length 10cms and width 10cms.

Area of a square = Length * width

A = 1*w

A = 10*10

A = 100cm

Example 2) Calculate the area of a square with length of each side as 20cms.

Area of a square = s²

A = 20²

A = 400cms

DIFFERENTIAL EQUATIONS

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivative of various orders. Differential equations are mathematically studied from several different perspectives, mostly concerned with their solutions—the set of functions that satisfy the equation. A partial differential equation (PDE) is a differential equation in which the unknown function is a function of multiple independent variables and the equation involves its partial derivatives.

A differential equation of the form where a, b, c are constants and q(x) is a function of x is called a second order linear differential equation with constant coefficients.

RANDOM VARIABLES

-->

A random variable is a function that associates a unique numerical value with every outcome of an experiment. The value of the random variable will vary from trial to trial as the experiment is repeated. A random variables have either an associated probability distribution (discrete random variable) or probability density function (continuous random variable). That's when we say that there are two types of Random Variables.

The expected value (or population mean) of a random variable indicates its average or central value. It is a useful summary value (a number) of the variable's distribution.

The (population) variance of a random variable is a non-negative number which gives an idea of how widely spread the values of the random variable are likely to be; the larger the variance, the more scattered the observations on average.

DISCRETE RANDOM VARIABLE:A discrete random variable is one which may take on only a countable number of distinct values such as 0,1,2,3,4,........ Discrete random variables are usually (but not necessarily) counts. If a random variable can take only a finite number of distinct values, then it must be discrete variable.

CONTINUOUS RANDOM VARIABLE: A continuous random variable is one which takes an infinite number of possible values. Continuous random variables are usually measurements. Examples include height, weight, the amount of sugar in an orange, the time required to run a mile. A continuous random variable is not defined at specific values.

SUBSETS

We all have learnt about sets, subsets and set theory. All these are interrelated to each other. Let us summarize about sets in this addition.

-->

SUBSETS

Below is a detailed meaning and explanation of Subsets.
If every element of a set B is also a member of a set A, then we say B is a subset of A. The relationship of one set being a subset of another is called inclusion or sometimes containment. The empty set is subsets of every set and every set is a subset of itself. The set C is called a proper subset of D , if C D and C/=D . In this case, we do not use C D . A set A is a proper subset of a set B if A is a subset of B but A is not equal to B.

Let us now see the formula in Math Subsets.

The number of subsets for a finite set A is given by the formula:

Number of subsets = 2 n(A)

where n(A) = number of elements in the finite set A

In mathematics, especially in set theory, a set A is a subset of a set B if A is "contained" inside B. A and B may coincide. The relationship of one set being a subset of another is called inclusion or sometimes containment.

Example : A = { 1,5,3,8,} , B = { 3,5} ,Here B is subset of A. That is B A

That's it for today will be back with more topics in math.