Importance of Statistics

Importance of Statistics

Statistics provides tools that you need in order to react intelligently to information you hear or read. In this sense, statistics is one of the most important subject matter that you ever study. Statistics play an important role in economics. Economics largely depends upon statistics. National income accounts are multipurpose indicators for the economists and administrators. Statistical methods are used for preparation of these accounts. In economics research statistical methods are used for collecting and analysis the data and testing hypothesis. These are the basics of Statistics.

Statistics plays a vital role in all the natural and social sciences. Statistics is a mathematics involving the collection, interpretation, analysis, and presentation of data. It is often used to make predictions based on data. It is playing a main role in calculations in science. The methods of natural sciences are most reliable but conclusions draw from them are only probable, because they are based on incomplete evidence. Statistical helps in describing these measurements more precisely.

Inferential statistics definition: Process of drawing information from sampled observations of a population and making conclusions about the population. Inferential statistics have a two-prong approach. To infer is to draw a conclusion from only partial evidence, such as a sample, so inferential statistics are techniques which may be used to evaluate the value of such conclusions; they tell us the probability of a statement based on a sample being valid for the whole population.

Circumference Of a Circle Formula

Today let us study about circumference of a circle formula.

The distance around a circle is called the circumference. The distance across a circle through the center is called the diameter. is the ratio of the circumference of a circle to the diameter. Thus, for any circle, if you divide the circumference by the diameter, you get a value close to . This relationship is expressed in the following formula: c/d= Π.
where is circumference and is diameter. Circumference, diameter and radii are measured in linear units, such as inches and centimeters.

Circumeference of a circle is calculated by the below formula

C = 2Πr

Where Π is equal to 3.14 and r is the radius.

Let us now solve some examples.

Example 1) What is the circumference of a circle with radius 5cms

Solution:

C = 2Πr

C = 2*3.14*5

C = 31.4

Example 2) What is the circumference of circles with radius 9cms

Solution:

C = 2Πr

C = 2*3.14*9

C = 56.52

AREA OF A TRIANGLE

Today’s topic is finding area of a triangle.

A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. The measures of the interior angles of a triangle always add up to 180 degrees. The sum of the lengths of any two sides of a triangle always exceeds the length of the third side. Two triangles are said to be similar if every angle of one triangle has the same measure as the corresponding angle in the other triangle. The corresponding sides of similar triangles have lengths that are in the same proportion, and this property is also sufficient to establish similarity.


Formula for area of a triangle

Area = 1/2base* height

Let us now try to solve some examples using the above formula.

Find area of a triangle with a base of 15 inches and a height of 4 inches.

Area = ½ (15*4)

= ½*60

= 30

Find the area of a triangle with a base of 9 inches and a height of 4 inches.

Area = ½ (9*4)

= ½ * 36

= 18

VOLUME OF CYLINDER FORMULA

A cylinder is one of the most basic curvilinear geometric shapes, the surface formed by the points at a fixed distance from a given straight line, the axis of the cylinder. A surface created by projecting a closed two-dimensional curve along an axis intersecting the plane of the curve. When the two-dimensional curve is a circle, the cylinder is called a circular cylinder. When the axis is perpendicular to the plane of the curve, the cylinder is called a right cylinder.

Volume of cylinder formula:-

V = Πr²*h

where r is the radius of the base and h is the height of the cylinder.

Cylindric sections are the intersections of cylinders with planes. An oblique cylinder has the top and bottom surfaces displaced from one another.

A cylinder generated by the revolution of a parallelogram other than a rectangle about one of its sides is known as a oblique circular cylinder. Parallelogram definition is A parallelogram is a quadrilateral with opposite sides parallel.

Volume of the oblique cylinder= BH cubic. Units

Where B is the area of the base and H is the height of the cylinder

When the two-dimensional curve is a circle, the cylinder is called a circular cylinder. When the axis is perpendicular to the plane of the curve, the cylinder is called a right cylinder. Learning Right Circulur cylinder is very easy if you know the bases of what is a Cylinder.

EQUILATERAL TRIANGLE

A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ABC.

There are different types of triangles. One among them that we will focus on today is Equilateral Triangle.
An equilateral triangle is a special isosceles triangle in which all three sides are congruent. Equilateral triangles are also equiangular, which means all three angles are congruent. The measure of each angle is 60 degrees. The figure below depicts an equilateral triangle with all the parts labeled.
Listed below are some rules that are to be kept in mind while dealing with isosceles and/or equilateral triangles.

1. If a triangle is equilateral, it is equiangular.

2. If two angles of a triangle are congruent, they are the base angles of an isosceles triangle.

3. If a triangle is equiangular, it is equilateral.

An equilateral triangle is the most symmetrical triangle, having 3 lines of reflection and rotational symmetry of order 3 about its center. Construction of triangles is very simple there are a few steps that you need to follow while you are constructing triangles.

WHAT IS ELEMANTARY ALGEBRA

Elementary Algebra is a work text that covers the traditional topics studied in a modern elementary algebra course. It is intended for students who

· have no exposure to elementary algebra,

· have previously had an unpleasant experience with elementary algebra,

· need to review algebraic concepts and techniques.

Elementary algebra generalizes arithmetic by treating quantities in the abstract. Thus where in an Arithmetic problem you may assert that 2+3 = 3+2 and that 4+1 = 1+4, in elementary algebra you assert that for any two numbers a,b we have a+b = b+a

To practice elementary algebra you will need to be first good at basic skills like addition, subtraction; multiplication and division of rational numbers and you must be able to use these operations on fractions. You must also have experience plotting points on a graph. Without these, you will not understand the operations required in elementary algebra. Ultimately, the goal of algebra is to calculate some unknown quantity, and the goal of elementary algebra is to solve the single-variable linear equation.

Elementary algebra questions could be as follows:

5-x = 3 or z7+a(b+x3)+42/y-π.

6 + 12x = 3 - 9x

You can also practice Elementary algebra questions and elementary algebra answers by clicking here

Learning Frustum

So far we have learnt about surface areas and volumes of combinations of two or more basic solids like right circular cone, right circular cylinder, sphere etc.. In this section , we shall learn about a solid which is a part of a right circular cone when it is cut by a plane parallel to the base of the cone. Such a solid is called a Frustum.

FRUSTUM: If a right circular cone is cut off by a plane parallel to its base, then the portion of the cone between the cutting plane and the base of the cone is called a frustum of the cone.

HEIGHT OF FRUSTUM: The height or thickness of a frustum is the perpendicular distance between its two circular bases.

SLANT HEIGHT: The slant height of a frustum of a right circular cone is the length of the line segment joining the extremities of two parallel radii, drawn in the same direction, of the two circular bases.

Construction of Incircle of a Triangle

Today we shall take down the steps involved in construction of Incircle of a Triangle.

Before that let us try to understand the concept of incircle. The name itself says it all.

Incircle of a Triangle: A circle touching all the sides of a triangle is known as Incircle of a Triangle.

The centre of the incircle of a triangle of the point of concurrency of the bisectors of any two angles of the triangle and its equidistant from the sides of the triangle. The centre of the incircle is called the incentre. If I is the incentre of a triangle ABC and ID is perpendicular, then length of the segment ID is called the in-radius of the circle.

Following steps are used to draw the incircle of a triangle.

Step 1:- Draw the given triangle, say ABC

Step 2:- Draw the bisectors of any two angles, say angle B, angle C of the triangle ABC

Step 3:- Obtain the point of intersection of the bisectors drawn in step 2. Suppose the bisectors intersect at a point, say O

Step 4:- Draw perpendicular from O on any side of the triangle, say OD on BC.

Step 5:- Taking O as centre and OD as radius draw a circle.

The Circle so obtained will touch all the sides of the triangle and it will be the required incircle.