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 Best Way Of Finding Highest Common Factor Of Numbers With Examples And Pictures

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HIGHEST COMMON FACTOR(HCF)


To start with, there are different methods of finding Highest Common Factor of numbers.

But;

what are factors?

A factor of a given number is a number that can divide the given number without a remainder. For instance, 2 can divide 6 without a remainder. Hence, 2 is a factor of 6.

How To Find The Factors Of A Given Number


Starting from 1, find all other numbers that can divide the given number without a remainder.

Example
Find the factors of 48

48 = 1 x 48
     = 2 x  24
     = 3 x 16
     = 4 x 12
     = 6 x 12

The numbers in bold text above are all factors of 48 because they can divide 48 without a remainder.

Thus factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

Little Tip: when looking for factors of an even number, just divide the even number by 2. The result is the highest factor you can have next to the given number.

E.g Find the factors of 24
Divide 24 by 2 which is 12. 
i.e 12 is the highest factor you can have next to 24.

Factors of 24 = 1, 2, 3, 4, 6, 8, 12 and 24



With our knowledge, let's find the HCF of these numbers using;

Method I


Example: 
Find the HCF of 8, 24 & 40

                                 Solution

Factors of 8:   1, 2, 4 and 8
Factors of 24: 1, 2, 3, 4, 6, 8, 12 and 24
Factors of 40: 1, 2, 4, 5, 8, 10, 20 and 40

The numbers in bold above are all Common in the three given numbers. There's a but here, we are looking for the Highest Common Factor here. So the HCF here out of 1, 2, 4, 8 is 8 obviously.

Thus HCF of 8, 24 and 40 = 8

Method II


Find the HCF of 8, 24 and 40.

                                 Solution
This is probably the simplest and fastest way of finding HCF. Here, we find a number that can divide all 3 numbers without any remainder. When you get to a point where you can not find a number that can divide all 3 numbers, you stop. Period, QED

Check the image below for simplified calculations



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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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