How to calculate deviation, variance and standard deviation

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 ...

Ratio: Examples,Comparison And Calculations

Having Trouble Learning Ratio?

Okay, your math teacher walked into your class with his belt on his tummy and his half shoe. Straight to the board he wrote #ratio and he turned with is already squeezed face saying "who among you knows ratio?" As usual, maths class is always silent as grave yard, No response. With frustration, he turned to the board and wrote what looks like jargons to you, explained in a shallow way, gave class work and you score zero. Well, here is another chance.

Ratio


Ratio is a comparison of two or more quantities that are alike.i.e you can't compare a dog to a book, same as you can't compare a car to a house. But you can compare a lorry to a truck in some way. The symbol for ratio is :

Example I|  2:3 is read as 2 ratio 3

Example 2| The ratio of red button to blue button will be red button:blue button.
       If you look closely, red button came first before blue button in the answer because red button came before blue button in the question.

NB: Ratios can also be written in fraction and vice versa i.e 2:3 = 2/3 but 2:3 is not equal to 3/2

Exercise 1

Complete to give equal ratios:

3 : 4 = [ ] : 16
Recall ratios can be written as fractions
• 3:4 can be written as 3/4
• [ ]:16 can be written as [ ]/16

I.e 3/4 = [ ]/16

Check the picture below for further and understandable calculation. 

Any trouble? Please let me know in the comment section.

Exercise II


Express each of these as ratio to the lowest term.
(a) 3cm : 36cm (b) 75k : N2 (c) 25min : 1h20min

Solution

(a) 3cm : 36cm

Ratio can be written in fraction
= 3/36
Lowest term = 1/12

Answer = 1cm : 12cm

(b) 75K : N2

Recall, you can't compare ratios with different unit. It's either you convert K(kobo) to N(naira) or N to K.
It's best you convert Naira to Kobo.
To do that;
We know 1 Naira = 100kobo
Therefore, 
2 Naira = 200kobo (so far N1 = 100k, N2 = 200k)

75K : 200K
They are both in Kobo, so we solve,

=75/200
Lowest term = 5/ 8

Answer= 5k : 8k

Check the picture below for simplified calculations

(3) 25mins : 1hr 20mins

As we already know, we can't work with mins and hour. They are not the same. So we convert hour to minutes.

1hr = 60 minutes

Therefore 1hr 20mins = 60 minutes + 20 minutes
 Which is 80 minutes.

1hr 20minutes = 80 minutes

They are both in minutes, so we can solve

25mins : 80mins
= 25/80

Lowest term= 5/16

Answer= 5mins : 16 minutes

Exercise III


Mr and mrs shuaibu bought some shares for their three children Jumai, Danladi and Kabiru in the ratio 7 : 5 : 3. If the total shares bought were 90000 units, how many units did each receive?

Solution


Recall, respectively i.e 

Jumai came first so as 7
Danladi came second so as 5
Kabiru came third so as 3

Parameters

Jumai = 7
Danladi = 5
Kabiru = 3

To solve, sum up the ratio. Which is 7 + 5 + 3 = 15
Total = 15


So far the question requests how much all recieved.
That will be

Jumai = Jumai/Total number of ratio x 90000

Danladi = Danladi/Total number of ratio x 90000

Kabiru = Kabiru/ Total number of ratio x 90000


Calculations

Jumai = 7/15 x 90000
            = 42,000 units

Danladi = 5/15 x 90000
              = 30,000 units

Kabiru = 3/15 x 90000
            = 18,000 units

i.e Jumai received 42,000 units
     Danladi recieved 30,000 units
     Kabiru recieved 18,000 units

Voila!!

Click here to continue the lesson on ratio

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Any question? Let me know in the comment section. I'll be using YouTube to post videos, although the link will be here for you to watch as i teach live. 



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