MEAN and MEDIAN

Example 1:

Find the mean deviation of the mean for the following data: 15, 17, 10, 13, 7, 18, 9, 6, 14, 11

Solution :

Let the mean of the given data be x1. Then,

i=1∑n|X1=x| / n

= [(120)/(10)] =12. [n=10]

The values of (x-x1 ) are 3,5,-2,1,-5,6,-3,-6,2,-1.

Therefore, the values are |x-x1| is 3,5,2,1,5,6,3,6,2,1

Mean Deviation (x1)=i=1∑n|x-x1| / n = 34/10=3.4

Hence Mean Deviation (x1)=3.4.

Example 2:

Find the mean and median for the data set: {8, 5, 13, 25, 49, 23, 27}

Solution:

Mean of data set:

Mean or average is the sum of all the observations in the set divided by total number of observations in a set.

Below is the formula for calculating Mean.

Mean = Total sum of data set / total number of elements in data set

= (8 + 5 + 13 + 25 + 49 + 23 + 27) / 5

= 150 / 5 = 30

Therefore mean is 30.

Median of the data set:

Median is the middle value of the data set after the arrangement in ascending or descending order.

Arrange the elements in ascending order: 5, 8, 13, 23, 25, 27, 49

Therefore median is 23.

IMPORTANT TERMS IN STATISTICS

The collection of data, its classification, tabulation and study is called Statistics. Most statistics can be used either as a descriptive statistic, or in an inductive analysis.

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Terms In Statistics:

• Quantitative Data: Quantitative data are data values that are numeric. For example, the heights of female basketball players are quantitative data values.

• Qualitative Data: Qualitative data are data values that can be placed into distinct categories, according to some characteristic or attribute. For example, the eye color of female basketball players is classified as qualitative data.

• Discrete Variables: Discrete variables are variables that assume values that can be counted-for example, the number of days it rained in your neighborhood for
  the month of March.

• Continuous Variables: Continuous variables are variables that can
  assume all values between any two given values-for example, the time it takes for you to
  do your Christmas shopping.

• Population: A population consists of all elements that are being studied. For example, we may be interested in studying the distribution of ACT math scores of freshmen at a college campus. In this case, the population will be the ACT math scores of all the freshmen on that particular campus.

How to solve Irrational numbers with out a calculator

In number theory tutorial, an irrational number is any real number that is not a rational number—that is, it is a number which cannot be expressed as a fraction m/n, where m and n are integers, with n non-zero,we have fractions calculator to find fractions if any. Informally, this means numbers that cannot be represented as simple fractions. Equivalently, irrational numbers are real numbers that cannot be represented as terminating or repeating decimals, and this presentation is often used in textbooks in elementary mathematics. As a consequence of Cantor's proof that the real numbers are uncountable (and the rationals countable) it follows that almost all real numbers are irrational. Perhaps the best-known irrational numbers are π, e and √2.we will also get rational expression calculator

Question:-

Simplify

 3√24 - 2√18
-------------
    -√2

Answer:-

 3√24 - 2√18
-------------
    -√2

3√12x2 - 2√9x2
--------------
    -√2

3√2 x √12 - 2 x 3√2
-------------------
     -√2

3√12 - 6
---------
   -1

= 6 - 3√12

= 6 - 3√4x3

= 6 - 3 x 2√3

= 6 - 6√3

= 6(1-√3)

How to find the raius of a circle

a radius of a circle or sphere is any line segment from its center to its perimeter. By extension, the radius of a circle or sphere is the length of any such segment, which is half the diameter.

Question:-

A sector of a circle has an area of 90 cm²and a central angle of 0.2radians .Find it's radius.


Answer:-

Area of sector = 90 cm²

Central angle = 0.2 radians

We need to convert this central angle to degrees

degrees=radians x 180/π

degrees=0.2 x 180/3.142

=11.5 degrees

                 11.5
Area of sector= -------- x area of the circle
                 360

    
             11.5
        90= ------ x πr2 
              360
The above step is having area of a circle formula
Let's find the radius (r) from the above equation

             90 x 360
            ---------- = r2
              11.5 π

          
             90 x 360
            ---------- = r2
             11.5x3.142


              896.8= r2


               r = √896.8 = 29.9

      So radius is approximately equal to 30 is the answer
We can use this in circumference of a circle formula to get the
circumference of the circle,similar ,if know the area of sector
for earth we can even find the radius of earth


                        

How to solve a linear equation

Topic : linear equation

When you enter an problem or equation into the calculator, the calculator will get the answer by simplifying the problem whether it is numerical or algebraic expression. Then it will attempt to solve the equation by using one or more of the the following : addition, subtraction, division, or by taking the square root of each side,factoring , and completing the square
This can be done with help of algebra calculator online two variables

Here are some example:

Question: Find X for the following 1.)-4 = 5 - 3x
Answer:

- 4 = 5 - 3x
5 - 3x = - 4
  - 3x = - 4 -5
  - 3x = - 9
     x = 3

2.) -2x -3 = 7

Answer:

- 2x - 3 = 7
- 2x = 7 + 3
- 2x = 10
   x = - 5

How to find the slope of a line

Slope is used to describe the steepness, incline, gradient, or grade of a straight line. 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. It is also always the same thing as how many rises in one run.

Question:-

In the xy-coordinate system,find the slope of a line which passes through origin and which is equidistant from two fixed points A(1,11)and B(7,7)

Answer:-

Let the slope of thr required line passing through origin be 'm' hence the equation of line is y=mx

So, mx-y=0

Since above line is equidistant from the points (1,11)and (7,7)

  m(1)-11     m(7)-7
--------- =  ----------
 √m2+1          √m2++1

m-11 = 7m-7

 m-11 = ±(7m-7)

m-11=+(7m-7) or -(7m-7)

If we solve futher

we get m= -2/3 or 2.25

Hence ,there is only one line satisfy in above condition with slope "1".

For more help on this ,you can reply me.
         

How to solve a simple linear equation

Topic:- Linear Equation


A mathematical expression that has an equal sign and linear expressions is called a Linear equation.

A number that you don't know,often represented by "x" or "y" is called a variable.

We solving linear equations by clicking and dragging a number to the "other" side of the equal sign. Remember that you are "isolating" the unknown "X" to solve the problem.
(Example is provided below.)

Question :-

Solve 2x-11=31

Answer:-

This math help is a part of linear equations.
   2x-11=31

 Add 11 on both sides


   2x-11+11=31+11

     2x=42

Divide by 2 on both sides

 2x     42
---- = ------
 2       2


 x=21

So 21 is the answer.

For more help on this ,Please reply me.