Mean, median, and mode

Hello everyone, thanks for coming again..

Now, i'm going to teach you how to do mean, median, and mode step by step.

First of all, i want to explain first what is mean by Mean, median, and mode.

Mean, median, and mode are three kinds of "averages". There are many "averages" in statistics, but these are, I think, the three most common, and are certainly the three you are most likely to encounter in your pre-statistics courses, if the topic comes up at all.

The "mean" is the "average" you're used to, where you add up all the numbers and then divide by the number of numbers.

The "median" is the "middle" value in the list of numbers. To find the median, your numbers have to be listed in numerical order, so you may have to rewrite your list first.
The "mode" is the value that occurs most often. If no number is repeated, then there is no mode for the list.

Practice Examples You will need paper, pencil and calculator.

1.	The weekly salaries of six employees at McDonalds are $140, $220, $90, $180, $140, $200.  For these six salaries,  find: (a) the mean (b) the median (c) the mode Mean:    90+ 140+ 140+ 180 + 200 + 220 =                                        6                         Median:    90,140,140,180,200,220 The two numbers that fall in the middle need to be averaged.     140 + 180 = 160  Mode:   The number that appears the most is 140
2.	Andy has grades of 84, 65, and 76 on three math tests.  What grade must he obtain on the next test to  have an average of exactly 80 for the four tests?84 + 65 + 76+ x   =   80(average) cross multiply                     4                                         and solve                         (4)(80) = 225 + x                              320 = 225 + x                            -225   -225                                95 = x                 Andy needs a 95 on his next test.
	3. In January of 2006, your family moved to a tropical climate.  For the year that followed, you recorded the  number of rainy days that occurred each month.   Your data contained 14, 14, 10, 12, 11, 13, 11, 11, 14, 10, 13, 8. a.  Find the mean, mode, median and range for your data set of rainy days. b.  If the number of rainy days doubles each month in the year 2007, what will be      the mean, mode, median and range for the 2007 data? c.  If, instead, there are three more rainy days per month in the year 2007, what will     be the me Answer mean mode median range a.) 11.75 11, 14 11.5 8 - 14 b.) 23.25 22, 28 23 16 - 28 Notice that if you double each data entry, you double the mean, mode, median and range. c.) 14.75 14, 17 14.5 11 - 17 Notice that if you add three to each data entry, you add three to the mean, mode, median and range.

linear inequalities (continue) Practices

linear inequalities (continue)

Practices

Question 1

Here, i will show you how to solve this problem step by step.

Step 1

2x - 5 < 1

We move -5 into 1 and then,we change the sign "-" become "+". Make 2x become single.

2x - 5 < 1

2x < 1 + 5

2x < 6

Step 2

We move 2 into another side and divide by 6 and make "x" become single.

2x - 5 < 1
2x < 1 + 5
2x < 6

x < 6 

      2

x < 3

So the answer is x < 3

Question 2

linear inequalities

linear inequalities

Hello all, thanks you for coming again :) Now I'm going to teach you the topic about linear inequalities. But, before that, did you know the meaning of linear inequalities??

Okey~ Now i'am going to tell what is mean by linear inequalities..

What is linear inequalities?

At Wikipedia said that In mathematics a linear inequality is an Inequalities which involves a linear function. A linear inequality contains one of the symbols of inequality:

• < is less than
• > is greater than
• ≤ is less than or equal to
• ≥ is greater than or equal to
• ≠ is not equal to

A linear inequality looks exactly like a linear equation, with the inequality sign replacing the equality sign.

Solving linear inequalities is almost exactly like solving linear equations.

1) Solve x + 3 < 0.

If they'd given me "x + 3 = 0", I'd have known how to solve: I would have subtracted 3 from both sides. I can do the same thing here:

So the answer is x < –3

2) Solve x - 3 ≤ 2

Step 1

Make "x" become single. mean..we move  "- 3" to the back of  "2"

Note : If we move "-" to the back, we must change the sign into "+" first!

x ≤ 2 + 3

Step 2

We add 2 and 3. The answer is 5

So, the answer is x ≤ 5

3) Solve 3(x+5) ≤ 2(x+1)

As you can see, this question is different from another question. Here, I will show you step by step.

Step 1

We open bracket first. We multiply 3 into X and 5 and multiply 2 into x and 1

3x(x) + 3x(5)  ≤ 2x(x) + 2x(1)

3x + 15  ≤ 2x + 2

Step 2

Then, we make "x" become one.We move +15 into 2x and then we move 2x into +15.

3x(x) + 3x(5)  ≤ 2x(x) + 2x(1)               

                                                    Note: When we move + 15 to anther side, we must change the                                                                           sign of "+" into "-" .

3x + 15  ≤ 2x + 2

3x - 2x ≤ -5 + 2

Then, we "-" 3x - 2x and "+" -5 + 2

3x - 2x = x

-5 + 2 = -13

So, the answer is x  ≤  -13

Working :

3(x+5) ≤ 2(x+1)

3x(x) + 3x(5)  ≤ 2x(x) + 2x(1)   

3x + 15  ≤  2x + 2

3x - 2x ≤ -5 + 2

x ≤  -13

logarithm (Practices)

Practices

Question and answer

Question 1

By applying the laws and Properties of logarithm, evaluate :

1. log39
2. log42

Answer

1) log39

~Log39 = x

~log3(x)  = 9

~3(x) = 9

~3(x) = 3(2)

~log39 = 2

Answer

2) log42

~log42 = x

~4(x) = 2(1)

~2(2x) = 1

~x = 1
        2
~log42 = 1
              2

Logarithm Example (Continue)

Example 1

What is x in log3(x)= 5 

log3(x)= 5
₃(5)= x
x = 243

~ 3 x 3 x 3 x 3 x 3

So the answer is x = 243

Example 2

Convert the following indices into logarithm form :-

1. 10² = 100
2. 15² = 225
3. 2² = 4
4. 5² = 25

Answer 1

Answer 2

log10(100)=2

10 x 10 = 100

log15(225) = 2

15 x 15 = 225

Answer 3

log2(4) = 2

2 x 2 = 4

Answer 4

log5(25) = 2

5 x 5 = 25

Logarithms

Okey everyone~ Now, I'm going to teach you how to do logarithm. But, before that we must know what is mean by logarithm first!

What is logarithm?

In mathematics, the logarithm is the inverse operation to exponentiation. That means the logarithm of a number is theexponent to which another fixed value, the base, must be raised to produce that number

Introduction to Logarithms

Example: How many 2s do we multiply to get 8?

Answer: 2 × 2 × 2 = 8, so we needed to multiply 3 of the 2s to get 8

So the logarithm is 3

Example 1:

Step 1

We write "the number of 2s we need to multiply to get 8 is 3" as:

log₂(8) = 3

So these two things are the same:

The number we are multiplying is called the "base", so we can say:

• "the logarithm of 8 with base 2 is 3"
• or "log base 2 of 8 is 3"
• or "the base-2 log of 8 is 3"

Notice we are dealing with three numbers:

• the base: the number we are multiplying (a "2" in the example above)
• how many times to use it in a multiplication (3 times, which is the logarithm)
• The number we want to get (an "8")

Example 2

Example: What is log₅(625) ... ?

We are asking "how many 5s need to be multiplied together to get 625?"

5 × 5 × 5 × 5 = 625, so we need 4 of the 5s

Answer: log₅(625) = 4

Example: What is log₂(64) ... ?

We are asking "how many 2s need to be multiplied together to get 64?"

2 × 2 × 2 × 2 × 2 × 2 = 64, so we need 6 of the 2s

Answer: log₂(64) = 6

Exponents

Exponents and Logarithms are related, let's find out how ...

The exponent says how many times to use the number in a multiplication. In this example: 23 = 2 × 2 × 2 = 8 (2 is used 3 times in a multiplication to get 8)

So a logarithm answers is like this:

In this way:

The logarithm tells us what the exponent is!

In that example the "base" is 2 and the "exponent" is 3:

So the logarithm answers the question:

What exponent do we need 
(for one number to become another number) ?

The general case is:

Example: What is log₁₀(100) ... ?

10² = 100

So an exponent of 2 is needed to make 10 into 100, and:

log₁₀(100) = 2

Example: What is log₃(81) ... ?

3⁴ = 81

So an exponent of 4 is needed to make 3 into 81, and:

log₃(81) = 4

 Another example :

This example is use the law  of logarithm to solve the following :

Example 1 : log_{32 +} log₃₅

 log_{32 +} log₃₅ 

Step 1

Change + into x first!

 log_32 x log₃₅ 

step 2,

Then multiply 2 and 5

log_32x5

So, the answer is log_32x5

= LOg₃₁₀

Geometric Progression

Hello..Hello.. and Helloooooooooo.................

Thank for coming again~

Here is a new topic that i will discuss with you all.

Topic : Geometric Progression

First of all, what is mean by Geometric Progression? Geometric Progression is a sequence of numbers in which each term is formed by multiplying the previous term by the same number or expression.

Formula for Geometric Progression :- 

Tn = ar(n-1)

r    = U3 = U2 = U4 = ................
         U2    U1    U3

S (infinity) = a
                     1-r

Here's some of the example of the Geometric Progression.

Example 1

Given the following numbers :-

3,-16,12,-2,........

a) Calculate the 27th term of the sequence.

Note
The question ask to calculate the 27th term of the sequence.

So, the first things you must do is find the difference between the two number.

Step 1

-6  = -2  , 12 = -2  
3             -16  

So r = -6      
           3
        = -2

We use formula of Tn = ar(n-1) to calculate the 27th term of the sequence.

Tn = ar(n-1)

Step 2

We identify first.

n = 27

a = 3

r = -2

Step 3

We include the number (number after we identify) into the formula.

Tn = ar(n-1)

T23 = 3 (-2)' 27-1

        = 3 (-2)' 26

        = 201326592

So, the 27th term of the sequence is 201326592.

Example 2

Given the following numbers :-

3,-16,12,-2,........

a) Find the sum of the series until the 32nd term.

Okay~ The question ask us to find the sum of the series until the 32nd term.

So, the first thing we must do is choesses the formula first. The question ask to find the sum of the series until the 32nd term. So that mean we use sum formula.

Sn = a (1-r'n ) 
            1-r

Step 1

Identify the number first.

n = 32

a = 3

r = -2

Step 2

Include the number into the formula.

Sn = a (1-r'n ) 
            1-r

Step 2

Input and calculate the number using formula to find the answer.

Sn = a (1-r'n ) 
            1-r

S32 = 3 (1-(-2)' 32)
               1-(-2)

Step 3

 S32 = 3 (1-(-2)' 32)  .............................. (- x - = + )
               1-(-2)          .............................. (- x - = + )

S32 = 3 (1 + 2)' 32)
                 1 + 2)
S32 = 3 [ 1 - 4294967296 ]
                       3

S32 = -4.294,967,296

So, the answer for the sum of the series until 32nd term is -4.294,967,296