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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[PICTURES] Having Problem On Fraction And Decimal Squares And Square Roots? I've Got You!

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SQUARE AND SQUARE ROOTS


SQUARE


Square number is the result of multiplying a number by itself. Example include:

2 x 2 = 2² = 4
3 x 3 = 3² = 9
4 x 4 = 4² = 16

Therefore, 4, 9, 16,... are square numbers because, these are numbers gotten from multiplying a number by itself.

How do you call it?;
2² { 2 raised to the power of 2 or 2-squared}
3² { 3 raised to the power of 2 or 3-squared}

Scroll down to view image with simplified calculation

EXAMPLE 1

Square Of Whole Numbers And Decimals


Evaluate each of the following;
(a) 220²  (b) 0.7²  (c) 10²

Solution

(a) 220² = 220 multiplied by itself
               = 220 x 220
 Answer = 48400

(b) 0.7² = 0.7 multiplied by itself
              = 0.7 x 0.7
Answer = 0.49

(c)  10² = 10 multiplied by itself
              = 10 x 10
Answer = 100


EXAMPLE 2

Square Of Fractions


Evaluate each of the following squared numbers;
(a) (5/11)²  (b) (2'3/16)²  (c) (2.7)²

Solution

The brackets means that all numbers inside it must be squared. Both the numerator and denominator.

(a) (5/11)² = (5 x 5)/(11 x 11) 
     Answer = 25/121


(b) (2'3/16)²
       This is a mixed fraction. Convert to improper fraction to solve.

 [2'3/16]² = [(16 x 2) + 3]/16
             = (35/16)²

We have successfully converted the mixed fraction to improve fraction. They are still the same

[2'3/16]² is the same as (35/16)²

(35/16)² = (35 x 35)/(16 x 16)
                = (1225/256)
  Answer = 4'201/256


(c) (2.7)² 
(2.7)² is also the same as (27/10)²

(27/10)² = (27 x 27)/(10 x 10)
                = (729)/(100)
  Answer = 7.29





SQUARE ROOT


Square root is the inverse (opposite) of squaring numbers.

12 x 12 = 144
√144 = √12 x 12 = 12.

EXAMPLE 1

Find the sqare root of the following numbers
(a) √400  (b) √900

Solution

There are different method you can use to find square root of numbers. But here is the simplest method. Factorization method.

View image for solution

(b)√900

View image for solution


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