Measure of Central Tendency

Measure of Central Tendency

What is Mean?
Mean is the most common measure of central tendency. It is simply the sum of the numbers divided by the number of numbers in a set of data. This is also known as average.

What is Median? Median is the number present in the middle when the numbers in a set of data are arranged in ascending or descending order. If the number of numbers in a data set is even, then the median is the mean of the two middle numbers.

What is Mode? Mode is the value that occurs most frequently in a set of data.

Examples & Questions :

Find the measures of central tendency for the data set 2, 7, 9, 4, 5, 4, 10, 7, and 3.

Example 1

You receive the pledge amounts listed below for your participation in a dance-a-thon. Which measure of central tendency best represents the pledge amounts listed?

       $1   $8   $12   $10   $45   $9   $1   $6

Example 2

Formula & Solutions ?

Sequence & Number Pattern

Example of Number Pattern

What is Number Pattern?

Number Pattern Explanation

Example & Questions:

Example of Arithmetic Sequence

Example of Geometric Sequence

Sequence

Explanation of Sequence

Example of Sequence

Examples & Questions :

How many dots will be there in the 6th diagram?

There will be 21 dots.

Formula & Solution

The Formula are :

x_n = n(n+1)/2 =

To find the next dots is a bit complicated because all you need to do is to indentify what is n used for?
n is represent as a 'diagram'. for example i need to find diagram 5, so make the n become 5 and used the formula that i mention on above. then you will exactly know the answer. You can draw any number pattern using matches, coins, rectangular and many more.

Logarithms

Example Law of Logarithms

How to Write Logarithm?

Example & Questions

Write the following  indices into logarithm form ?

Example 1

Solutions :

With these problems you have to convert it first

1st Step : Move the power become answer
2nd Step : Answer will become power
3rd Step : The base will become "Log (any value)"

Write the following logarithm into indices form ?

Example 2

Solutions :

With these problems you have to convert it become indices, same thing like example 1.

1st Step : Move the answer become Power
2nd Step : Power will become answer
3rd Step : The base will become normal value with power.


Solve the equation

Example 3

Solutions :

If you see something like this equation, first you have to convert it to indices form so that it easy to evaluate. Once you convert, find the like terms and eliminate like 4 & 81. Then once you get the answer, you can calculate it as usual.




Express as a single logarithm ?

Example 4

Solutions :

Since all the value are almost the same, so all you need to do is just change the operation like plus become multiply whereas minus become divide. After everything change, then calculate is as usual.

Inequalities

Symbols of Inequality

What is Inequalities?

As you can see on the image below, it indicates the Symbol and Arrow with difference direction.

The Difference between this 4 lines are only  the direction & shaded circle.

Exanples & Questions

Example 1

As you can see on the picture above it shows the final answer already which is X is greater than 3. Then you may start using the graphing inequalities. And you must point the arrow to the right because the inequalities sign '>' facing to the right.

Example 2

This example 2 shows an equation and different inequality sign that you have to solve. First thing you have to make the variable 'x' is alone, so since no 5 had the same character with number 7, you have to bring no 5 to the right side along with the plus sign but instead of plus sign, you have to changed it become minus. Then you free to solve. Plus, as you can see the inequality sign is different than before, because there's a underline. so with this inequality sign ≤
you have to shaded the circle and then you free to draw the line after you solve the problem.

Example 3

  This example 3 is a bit hard than the previous example, because as you can see there were two equation. So first thing you need to find is the like terms, once you find then you calculate as usual. But the thing is there's a  negative sign with the variable 'x'. We want to be x is alone. So bring the '-' to the right side then it will be -4. Plus as you can see the final answer the inequality sign changing its direction because of changing inequalities sign multiply or divide with a inequality sign.

Example 4

Last example is a bit confusing because the question provide 2 inequality symbol. So with this problem all you need to do is find the like term first and then calculate. after you solve everything, here's the thing there are two unshaded circle because there are 2 inequality sign, so connect the line together and make unshaded circle left and right side. And that's it.

Solve?

 Our main points is to have 'x' or  whatever the variable is with the left of inequality sign for example
x > 5 (so we called this one is final answer)

Safe Things To Do

These are things we can do without affecting the direction of the inequality:

Add (or subtract) a number from both sides
Multiply (or divide) both sides by a positive number
Simplify a side

Set Theory

Venn Diagram

What are the SETS?

U or Є = Universal Set

Ε = Elements or Belongs to

Ɇ = Does not belong to

∩ = Intersection

U = Union

Φ or {} = Empty Set

Examples & Question:

Venn Diagram (1st example)

1  A travel agent surveyed 100 people to find out how many of them had visited the districts of Brunei Muara, Tutong and Belait. It is shown in the Venn Diagram below.

 

From the Venn diagram, find the number of people who had visited

a)      Brunei Muara and Tutong

2+4= 6 people

b)      Tutong but not Belait

2+16= 18 people

c)       Brunei Muara only

38 people

d)      None of the districts

20 people

 

Venn Diagram 2nd example

 

From the diagram above, state what is :-

              n (A n B n C) = 4

              n (A n C) = 6 + 4 = 10

              n (A n B) = 4 + 2 = 6

 Formula & Solution ?

 The formula of using Venn diagram are the 'sets' that i have mention on above. For example in Question 1, it asked what is the total between Brunei Muara & Tutong? so to solve this problem its easy, what is the intersect between these two districts. So the intersect are 2 & 4. Then you have to add together this two value. Once you add then you finally found the answer. Same thing like question no.2, but in example 2 they already give the sets between the 3 letters. So all you need to do just focus what is the intersect between these 3 letters (depend what the question ask you what to find)