Median, Mean, Mode and Range

Median
The middle number (in a sorted list of numbers). To find the Median, place the numbers you are given in value order and find the middle number. Example: find the Median of {13, 23, 11, 16, 15, 10, 26}. Put them in order: {10, 11, 13, 15, 16, 23, 26} The middle number is 15, so the median is 15. (If there are two middle numbers, you average them.)

Finding the Mode

To find the mode, or modal value, first put the numbers in order, then count how many of each number.

Example:

3, 7, 5, 13, 20, 23, 39, 23, 40, 23, 14, 12, 56, 23, 29

In order these numbers are:

3, 5, 7, 12, 13, 14, 20, 23, 23, 23, 23, 29, 39, 40, 56

This makes it easy to see which numbers appear most often.

In this case the mode is 23.

How to Find the Mean

The mean is the average of the numbers.

It is easy to calculate: add up all the numbers, then divide by how many numbers there are.

In other words it is the sum divided by the count.

Example 1: What is the Mean of these numbers?

6, 11, 7

• Add the numbers: 6 + 11 + 7 = 24
• Divide by how many numbers (there are 3 numbers): 24 / 3 = 8

The Mean is 8

The Range (Statistics)

The Range is the difference between the lowest and highest values.

Example: In {4, 6, 9, 3, 7} the lowest value is 3, and the highest is 9.

So the range is 9-3 = 6.

It is that simple!

But perhaps too simple ...

The Range Can Be Misleading

The range can sometimes be misleading when there are extremely high or low values.

Example: In {8, 11, 5, 9, 7, 6, 3616}:

• the lowest value is 5,
• and the highest is 3616,

So the range is 3616-5 = 3611.

The single value of 3616 makes the range large, but most values are around 10.

Pre- Algebra

- Geogebra

What is GeoGebra?

- GeoGebra is an interactive geometry, algebra, and calculus application, intended for teachers and students. Most parts of GeoGebra are free software.

Which is its use?

- It’s for us to make geometric figures without any mistakes really easy and is really useful for teachers, students and all that has to be about geometric figures, polygons, etc.

How to do a polygon  with Geogebra:

https://www.youtube.com/watch?v=tyFsAykHkTU

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Pre - Algebra

Types of angles

o   Acute angle

An acute angle is an angle whose measure is less than 90 degrees.

o   Right Angle

A right angle is an angle whose 90 degrees.

o   Obtuse Angle

An obtuse angle is an angle whose measure is bigger than 90 degrees but less than 180 degrees.

o   Straight Angle

A straight angle is an angle whose measure is bigger than 180 degrees.

o   Reflex Angle

An angle whose measure is bigger than 180 degrees but less than 360 degrees.

o   Adjacent Angle

An adjacent angle is an angle with a common vertex and one common side.

o   Supplementary Angle

Supplementary angles that have two angles whose measure have 180 degrees.

o   Complementary Angle

A supplementary angle that has two angles whose measures add to 180 degrees.

o   Vertical Angle

Are angles that have a common vertex and whose sides are formed by the same lines.

o   Alternate Interior Angles

Are pairs of interior angles on opposite sides of the transversal.

o   Alternate Exterior Angles

Are pairs of exterior angles on opposite sides of the transversal.

o   Corresponding Angles

Corresponding angles are pairs of angles that are in similar positions.

Pre-Algebra

Divisibility Rules

Divisibility Rules for 2

1.     All even numbers are divisible by 2. E.g., all numbers ending in 0,2,4,6 or 8.

Ex.228

 Divisibility Rules for 3

1.  Add up all the digits in the number.

2.  Find out what the sum is. If the sum is divisible by 3, so is the number.

Ex.3345

Divisibility Rules for 4

1.     The last two digits are divisible by 4.

Ex. 812

Divisibility Rules for 5

1.     Numbers ending in a 5 or a 0 are always divisible by 5.

Ex. 500

Divisibility Rules for 6

1.     The number is divisible by both 2 and 3.

Ex. 114

Divisibility Rules for 9

1.   Add up all the digits in the number.

2.  Find out what the sum is. If the sum is divisible by 9, so is the number.

Ex. 9432

Physical Science

Review 3.1 (Gravity) 
Problem pg. 83 

6. Synthesize

 Presicion measurements of the acceleration due to gravity show that the acceleration is          slightly different in different locations on Earth. Explain why the force of gravity is not            exactly the same everywhere on  Earth's surface. Hint: Think about the details on Earth's      surface.

Answer:
Because of different elevations in Earth.

Review 3.2 (Friction) 
Problem pg.89

6. Synthesize

If you push a book against a wall hard enough, it will not slide down even though gravity is     pulling it. Use what you know about friction and newton's laws of motion to explain                   why the book does not fall.

 Answer:
It doesnt fall because you are pushing it to the wall and thewall is pushing it to you, in result are holding the object up so it doesnt fall.

Review 3.3 (Pressure)
Problem pg. 83

6. Synthesize

During cold winters, ice can form on small lakes and ponds.  Many people skates on thin ice and breaks  through it. Why do rescue workers lie flat on the ice instead of walking upright when reaching out to help rescue skater?

Answer:
Because the weight of the rescuer is divide in a bigger area and preasure is less because of this.

 Geometry
 Is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

The basics concepts of geography are:

-Point
 A point has no length, width, or height - it just specifies an exact location. It is zero-dimensional.
Every point needs a name. To name a point, we can use a single capital letter. The following is a diagram of points A, B, and M:

-Line
A line is as wide as a point, infinitely thin, having an infinite number of points, (in a straight row), extending forever in both the directions. Any two lines can intersect at only a single point.

-Line Segments
A line segment, or segment, is a part of a line, which has two endpoints. The endpoints give the line segment a fixed, or finite length.

-Ray
A ray is a line segment that has only one endpoint. A ray is infinite in one direction. That means that it goes on forever in one direction. 

-Midpoints
The midpoint of a segment divides the segment into two segments of equal length. 
The midpoint will be in the middle of A and B. Since M means midpoint.

-Planes
Planes are two-dimensional. A plane has length and width, but no height, and extends infinitely on all sides. Planes are thought of as flat surfaces, like a tabletop. A plane is made up of an infinite amount of lines. Two-dimensional figures are called plane figures.
All the points and lines that lie on the same plane are said to be coplanar.

-Space
Space is the set of all points in the three dimensions - length, width and height. It is made up of an infinite number of planes. Figures in space are called solids.

-Angles
An angle  is a figure by two rays with a common endpoint, and which are not in the same  point.