How to calculate deviation, variance and standard deviation

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Dispersion and variation Dispersion and variation are words that are used to describe the spread of values in a given set of data. Before you proceed, I recommend you check this post out, it's a prerequisite. Consider the set of examination marks of ten students in the  image below The marks are the same. They do not vary. No dispersion. Check the image below You can see that the marks are not the same. They vary. Their mean is 60. Some of the marks are greater than 60 while others are less. This set of marks has a greater variation or dispersion than those in table 1 Also, consider this table which shows a third set of marks of ten students. Although the mean is also 60. Don't know how to calculate mean? click here . However, it is clear that the marks are more varied than those in table 2. Thus, the marks here have a greater dispersion than the other marks. Let's talk about range. Range The range of a set of numbers is the difference between the
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The simplest way of solving quadratic equations

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Algebraic Process: Quadratic Equation


By the end of this post, you should be able to solve quadratic equations by:

i. Factorisation
ii. Completing the square
iii. Quadratic formula.

Consider this;

If the product of two real numbers is 0, then one of the number or both of them must be 0.

In general,

If a x b = 0
Either a = 0 or b = 0

Example 1


Solve the equation (x - 4)(x + 9) = 0
If (x - 4)(x + 9) = 0

Then either 
x - 4 = 0    Or     x + 9 = 0
x = 4         Or     x = -9


Example 2: Using Factorisation


Solve 2x² + 13x = 15

First thing here is to equate it zero by carrying +15 to LHS (Left Hand Side)

2x² + 13x - 15 = 0

If you notice, +15 changed to -15 when carried to LHS because, it's crossed the "=" sign.

Now, the above equation can be solved in two ways;
factorisation or quadratic equation

2x² + 13x - 15 = 0

Can be factorised to get

2x² + 15x - 2x - 15 = 0
x(2x + 15) -1(2x + 15) = 0
(2x + 15)(x - 1) = 0

Then,
2x + 15 = 0          or      x - 1 = 0
2x = -15               or      x = 1
x = (-15/2)
x = -7½                or      x = 1

Quadratic Equation


Before we delve into quadratic equation, we must shed a little light on completing the square

Completing the square


Example 

What must be added to d² - 5d to make the expression a perfect square?

Solution

The coefficient of d is -5. 

Divide -5 by 2 which is -5/2.

(-5/2)²

= +25/4

That means, +25/4 must be added to d² - 5d to make it a perfect square.

d² - 5d + 25/4

It becomes simpler when you go over it again. Probably these steps might help;

i. Find the coefficient of the non-squared term
ii. Divide it by 2
iii. Add the result to the question....Viola

Back to quadratic equation


The general form of a quadratic equation is
ax² + bx + c = 0. The  roots of the general quadratic equation are found by completing the square.

Check the image below:

This is called the quadratic formula. Use the formula to solve any quadratic equation.


Consider this example

Find the roots of the equation 3x² - 5x - 7 = 0.

Check the image below for simplified calculation

quadratic equation Learnmathwithpelumi

That's all for now, please comment and share your thoughts. Any question will surely be answered.

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Hi there, I'm a student like you who studied mechanical engineering and also aiming for software engineering. I'm here to walk you through basic and elementary mathematics. I'll give you the knowledge and foundation you need in a simplified way to build on and become a math geek you've always wanted to be. Like, share and follow for more videos

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