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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Don't Know Ratio Yet? Check Me Out, I've Got You!

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 More Examples On Ratio


We started ratio this week and we've learnt some interesting examples on ratio. Interested in the previous lesson? click here to see previous lesson on ratio and also view our table of content here

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Example 4

In a school gathering, the ratio of boys to girls was 4: 5. There were 32 boys.

(a) How many are girls?

(b) How many people were there altogether?

(c) What is the ratio of;

      i. Girls to boys

      ii. Girls to total people

Scroll down to view image with simplified calculation

                              Solution


Parameters 

Ratio

Boys = 4

Girls = 5

Total = 4 + 5 = 9

Nõ of students

Boys = 32

Girls = ? (G)

Total = ? (T)


To start with, lets find the total number of students (T) by solving the ratio of boys in the normal way.


Total nõ of boys = (ratio of boys/Total ratio) x Total number of students


32 = (4/9) x T

32 = 4T/9

4T = 32 x 9

4T = 288

Divide both sides by 4

Hence, T = 72

Total number of students = 72



(a) How many are girls?


In a school, we all know it consists of boys and girls. We know boys to be 32 and the total number of students to be 72


Total nõ of students =Boys + Girls

72 = 32 + G

Collect like terms

G = 72 - 32

G = 40


Therefore total nõ of girls = 40


(b) How many people were there altogether?


That is total number of students which is 72


(c) What is the ratio of;


      i. Girls to Boys

Ratio of girls = 5

Ratio of boys = 4

= 5 : 4 (respectively)


      ii. Girls to total people

Ratio of girls = 5

Ratio of total people = 72

= 5 : 72 (respectively)


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