MATHEMATICS

  TYPICAL HISTOGRAM SHAPES AND WHAT THEY MEAN Normal Distribution A common pattern is the bell-shaped curve known as the "normal distribution." In a normal or "typical" distribution, points are as likely to occur on one side of the average as on the other. Note that other distributions look similar to the normal distribution. Statistical calculations must be used to prove a normal distribution. It's important to note that "normal" refers to the typical distribution for a particular process. For example, many processes have a natural limit on one side and will produce skewed distributions. This is normal—meaning typical—for those processes, even if the distribution isn’t considered "normal." Skewed Distribution The skewed distribution is asymmetrical because a natural limit prevents outcomes on one side. The distribution’s peak is off center toward the limit and a tail stretches away from it. For example, a distribution of analyses of a very p...

  WHAT IS A HISTOGRAM? A frequency distribution shows how often each different value in a set of data occurs. A histogram is the most commonly used graph to show frequency distributions. It looks very much like a bar chart, but there are important differences between them. This helpful  data collection and analysis tool  is considered one of the  seven basic quality tools . Histograms vs. Bar Charts Both histograms and bar charts provide a visual display using columns, and people often use the terms interchangeably. More technically, a histogram represents the frequency distribution of variables in a data set. On the other hand, a bar graph typically represents a graphical comparison of discrete or categorical variables. WHEN TO USE A HISTOGRAM Use a histogram when: The data are numerical You want to see the shape of the data’s distribution, especially when determining whether the output of a process is distributed approximately normally Analyzing whether a process c...

  The Real Number System All numbers that will be mentioned in this lesson belong to the set of the Real numbers. The set of the real numbers is denoted by the symbol  \mathbb{R} R . There are  five subsets  within the set of real numbers. Let’s go over each one of them. Five (5) Subsets of Real Numbers 1) The Set of Natural or Counting Numbers   The set of the natural numbers (also known as counting numbers) contains the elements, The ellipsis “…” signifies that the numbers go on forever in that pattern. 2) The Set of Whole Numbers  The set of whole numbers includes all the elements of the natural numbers plus the number zero ( 0 ). The slight addition of the element zero to the set of natural numbers generates the new set of whole numbers. Simple as that! 3) The Set of Integers The set of integers includes all the elements of the set of whole numbers and the opposites or “negatives” of all the elements of the set of counting numbers. 4) The Set of R...

  TYPES OF TRIANGLE  TRIANGLE:  A triangle is a polygon with three edges and three                                vertices.                   It is one of the basic shapes in geometry.                     A triangle with vertices A,B and C is denoted. TYPES OF TRIANGLE: AREA OF TRIANGLE:

2D AND 3D SHAPES SHAPES:  The shape can be defined as the boundary or outline of an object. In general, we can see shapes such as triangles, squares, and circles everywhere around us. Thus shapes have only lenght and breadth are 2D or two-dimensional. while other shapes such as the shape of a house have length, breadth and height. Thus shapes are 3D or three-dimensional. 2D SHAPES:                           A 2D shapes has two dimensions lenght and breadth. examples: Rectangle, Square, Circle, Triangle. 3D SHAPES:                        A 2D shapes has three dimensions lenght, breadth and height. examples: Cuboid, Cube, Cylinder, Sphere. See the above image the 1st one is circle and it is in 2D shape and the 2nd one is sphere and it is in 3D shape. Here are some 2d and 3d shapes Differences between 2D and 3D shapes You (or the children in your class) mig...

  CONCENTRIC AND CONGRUENT CIRCLES CIRCLE: A circle is the set of points in a plane that are equidistant from a given point. CONCENTRIC CIRCLE: Two or more circles that have the same center,but different radii are known as concentric circles. Concentric Circle Examples In Real Life Have you ever observed the wheel of a ship? It has two concentric circles joined by the spokes. Many of us have played darts. A dartboard also has concentric circles. The circles in the dartboard are drawn around a common center, that is, the bull's eye. CONGRUENT CIRCLE: Two or more circles with the same radius,but different centres are known as congruent circles.

  SET AND TYPES OF SETS SET: A set s well defined collection of objects or numbers or elements. UNION OF SET: The union of two sets is a set containing all elements that are in A or in B. INTERSECTION OF SET: Intersection of two given sets is the largest set which contains all the elements that are common to both the sets. TYPES OF SETS 1. Empty Sets The set, which has no elements, is also called a null set or void set. It is denoted by {}.Below are the two examples of the empty set. Example of empty set: Let set A = {a: a is the number of students studying in Class 6th and Class 7th}. As we all know, a student cannot learn in two classes, therefore set A is an empty set. Another example of an empty set is  set B = {a: 1 < a < 2, a is a natural number}, we know a natural number cannot be a decimal, therefore set B is a null set or empty set. 2. Singleton Sets The set which has just one element is named a singleton set. For example,Set A = { 8 } is a singleton set. 3. Fi...