Best Measure of Central Tendency

What are Measures of Central Tendency?
Central tendency refers to the centre value of the data. Measures of the Central Tendency calculate the central or middle value or the average of the given data. This is different from the measures of dispersion, which tells about the spread of the data values around the average.  We can thus define Measures of Central Tendency as the methods of measuring the central tendency of the given data. There are various measures of the central tendency. The measures of the central tendency are mean, median and mode. Each of these measures differs in the way they calculate the central tendency or average of the given data.

The method of calculating mathematical average is termed as arithmetic mean. The measure that finds out the value which is present half-way in the data arranged in ascending order is termed as median. Most frequently occurring data is called as mode.

Features of Measures of Central Tendency
• For a normal data set, all the three measures give equal results.
• Unlike mode, the mean and median have only one value as the result.

Best Measure of Central Tendency
The best measure of central tendency depends upon the given data set, situation and the nature of analysis for which the central tendency has to be calculated. Let us see different situations and the appropriate measure of central tendency that is best suited for those situations.

Mean, Median or Mode
Any one of the three measures of central tendency mean, median or mode can be used to calculate the central tendency in case below:
• Data set containing numerical data or interval data.
• Data set containing continuous data.

Mean
It is the commonly used measure of central tendency for:
• Data set having mathematical data values.
• Data set used for statistical calculations or interference.
• Data set having no extreme values.
• Data set having symmetrical values.

Median
The data sets whose central tendency is to be measured using median are:
• Data set containing random numbers.
• Data set containing different numbers.
• Data set containing extreme values.
• Data set containing ordinal data or ranked data.

Mode
The data set whose central tendency is to be measured using mode are:
• Data set containing values that are closer or equal in value.
• Data set containing nominal data. Mode is the only measure of central tendency to measure nominal data or qualitative data.   For example, Marital status

There are two scenarios when either median or mode can be applied. They are:
• Data set containing outliers
• Data set where data is skewed

Introduction to Basic Algebra For Kids

Algebra is the main part of mathematics in which symbols or signs such as letters of the alphabet which stands for the numbers. The following algebra based on the kids only.

There are two opposite sets of numbers: one is positive numbers and another is negative numbers.

Positive Numbers:

All positive integer numbers are the positive numbers. It is including the plus sign. The numbers are called co efficient and x is the variable.

Example: x, 2x, 3x, 4x, 5x…

Negative Numbers:

The Negative numbers must go to the left and the positive to the right. While the negative numbers are always written in a minus sign in front of them, the positive numbers do not represent always sign in front of them.

Example: -x,-2x,-3x …

Basic Algebra for Kids Addition and Subtraction:

Adding and Subtracting of two numbers:

The Addition basic algebra is the adding the positive numbers or negative numbers. If the both numbers are positive numbers or negative numbers adding the algebra expression.

Basic Algebra kids example for addition:

3x + 4x = -7y –y

7x = -6y

7x + 6y = 0

The subtraction of basic algebra for kids it is the subtracting the positive numbers to negative numbers or negative numbers to positive numbers.

Basic Algebra kids example for subtraction:

4x-3x = 6y – 7y

x = -y

x + y=0

Multiplication and Division of Basic Algebra Numbers for Kids:

The multiplication of positive and negative numbers has some rules which depend on the equation. It is also called simplifying.

Example for Basic Algebra kids multiplication:

(2x + 3) (3x + 2)

(2x)(3x + 2) + (3) (3x + 2)

6x2+4x = 9x +6

6x2 +4x -9x -6 = 0

6x2 – 5x -6 =0

Dividing of two numbers:

Dividing positive and negative numbers has certain special rules. The division is containing divisor, quotient, and remainder.

Example for Basic Algebra kids Division:

(4x + 6) / (2x+3)

2x+3) 4x + 6 (2
4x + 6
-----------
0
-----------

Introduction of slope in math

In mathematics, the slope or incline of a line describes its steepness, incline, or grade. A higher slope value indicates a steeper incline.

The slope is defined as the ratio of the "rise" divided by the "run" between two points on a line, or in other words, the ratio of the altitude change to the horizontal distance between any two points on the line. Given two points (x1,y1) and (x2,y2) on a line, the slope m of the line is

m=`(y2-y1)/ (x2-x1)`

(Source: Wikipedia)

Definition of Constant Slope in Math:

In math, to finding constant slope to build up a slope formula. To begin, we choose points P and Q on the line. To distinguish between the corresponding of these points, we use subscript notation. Point P has coordinates (x1,y1) and point Q has coordinated(x2.y2).

As we move from point P to point Q, the rise is the dissimilarity of the x-coordinates:x2-x1, as the constant slope is the ratio `(rise) / (run)` ,  we have the following formula for calculating constant slope.

In math, another notation that we use to describe constant slope involves the symbol ∆, which is the letter delta from the Greek alphabet. If the modify in y is represented by ∆y and the change in x is represented by ∆x, then:

M=`(Deltay) /(Deltax)` where ∆x≠0

The entire notation associated with the concept of constant slope of a line.

Example for Constant Slope in Math:

In math, find the constant slope of the line passing through (-1,2) and (3,-4)

Strategy we will use the constant slope formula to find the constant slope.

Why?  We  know the coordinates of two points on the line.

Solution:

We can let(x1,y1)=(-1,2) and (x2,y2)=(3,-4). Then we have

m=`(y2-y1)/(x2-x1)` this is the constant slope formula.

=`(-4-2)/(3-(-1))`      substitute -4 for y2, 2 for y1,3 for x2, and -1 for x1.

=`(-6/4)`

=`-3/2`

Write `(-3/2)` with the – sign in front of the fraction. The outcome is negative.

The constant slope of the line is `-3/2`

In math, the line passing through (-1,2) and (3,-4) points. Notice that we obtain the same result when the constant slope of the line is

m=`(rise)/(run)`=`-3/2`

Basic geometric shapes

Geometry is a module of math which involves about the study of shapes, lines, angles, dimensions, etc. it plays vital role real time application like elevation, projection. here some content have given about basics geometry shapes. The basics geometric shapes are circle, triangle, rectangle, square.In practical geometry, we do not construct exactly the geometrical shapes but draw rough sketches of the shapes to give support to our logical reasoning.

Basic Geometric Shapes: Circle

When a point P moves in a plane in such a way that its distance remains constant from a fixed point (say C). The figure thus formed is called a circle.it is one of the basics shapes in geometry. The fixed point is called the centre of the circle and the distance between the moving point (P) and the centre (C) is called the radius of the circle.

Basic Geometric Shapes: Triangle

The triangle is a closed figure formed by three line segments. Make three points A, B, C not on the Same line. Draw the line segments AB, BC and AC .The figure formed is called triangle ABC. The symbol Δ is used to denote the triangle. Thus ΔABC is read as triangle ABC. The points A, B, C is called the vertexes of the triangle ABC.

Basic Geometric Shapes: Rectangle

In a quadrilateral, if opposite sides are equal and all the four angles are equal to right angle then it is called a rectangle. The rectangle is also one type of parallelogram, whose one of the angles is a right angle. In the figure ABCD is a rectangle AB and CD as also AD, and BC are its two pairs of opposite sides, and A, C and B, D are its two pairs of opposite Angles.

Basic Geometric Shapes: Square

In a quadrilateral if all the four sides are equal and if all the angles are right angle then the quadrilateral is called a square. a square is a rectangle, with a pair of adjacent sides equal . ABCD is a square. Since, it is also a rectangle. Therefore, AB = CD and AD = BC .A = B = C = D = 90° AC = BD Since its adjacent sides are equal.

Introduction to base of a triangle

The base of a triangle is that side of the 3 sides of a triangle which one is the perpendicular to the altitude.
There are many kind of triangles, they are categorized as Equilateral triangle (3 of whose sides are equal in length and each angle is 60o   ), Isosceles triangle (Two of whose sides are equal in length), Scalene (none of whose sides or angles are equal)

Now, Isosceles triangles are also have further divided into some categories, those are – Acute angled, right angled, obtuse angled. Scalene triangles are also have further divided into some categories - those are – Acute angled, right angled, obtuse angled.

Various Kinds of Triangles and the Circulation of their Bases

Right angled triangle and its base :

First we will  deal with the easiest one -  the right angled triangle . the picture below describes the base of a triangle

b - base of the triangle.

Base of a EquilateralTriangle :

This kind of triangle has a typical story . Any one  of the 3  sides can be taken as a base if we do  rotate the triangle keeping any  of the sides perpendicular to the altitude.

Base of a Scalenetriangle:

The side perpendicular to the base is called the base of the triangle.

Here b is the base of the triangle.

Example Problems - Base of a Triangle:

1)Find the base of the equilateral triangle shown below

solution for base of a triangle:

given side = 5 and Height = 4

consider one half of the triangle,

by using Pythagoras theorem,

a^2=b^2+c^2

b =`sqrt(a^2-c^2)`

b = `sqrt(25 -16)`

b = `sqrt(9)`

b = 3.

Therefore the base 2b = 6

6 is the base of the triangle.

2) Find the base of the triangle shown below

The given figure is a right angled triangle.

So we use Pythagorean theorem,

a^2=b^2+c^2

b =`sqrt(a^2-c^2)`

b = `sqrt(625 -46)`

b = `sqrt(576)`

b = 24.