HOW TO SOLVE QUANTILE PROBLEMS

Wednesday, January 31, 2018

   QUANTILES

          A statistical term. Quantiles is a generic term for cut-off points. A universal picture telling us how we split the string. If we are talking one straight line for example which measures 100 feet, we can cut it off by 10's, 20's, or by 25's, etc. When we are cutting the said straight line by 10's we can say we are cutting it in :decile". Or if cut it off by 25's we are doing quartile-cut. We can also do cutting foot by foot to make it 100 cuts for percentile.

         Quantiles has three types. The quartiles, which is 25% per size, decile which 10%  per size, and percentile which 1% per size. Quantiles is used either in "Grouped data" or "Ungrouped Data".

         We use quantiles in Statistics if we are resizing the data in the desired size we want. We use quartiles if we need to separate data in four equal parts, decile and percentile for 10's and 1's respectively. We have formulae for that as to resize. The formula for "Ungrouped data" is different from "Grouped data". 

Here is the formula for "Ungrouped data"

For Percentile:

For Quartile:

For Decile:

Illustrative examples:

Given the following data.

4, 2, 5, 6, 9, 10, 3, 7, 9, 12, 8, 15

Solve for the following Percentiles:

(In Percentile problem, we can assign values for k from 1 - 100). In this problem. we will use only 5 problem for Percentile. We will use 20th, 34th, 67th, 50th,25th Percentile. In some cases, you can use any kth percentile. But mostly, we do not solve for the 100th Percentile.

1. 20th Percentile

Formula: P = 20 (n + 1) / 100

Given: 
  
k = 20 (desired size)
n = 12 (number of data we have)

Required: P20

Solution:

P = k (n + 1) / 100

P = 20 (12 + 1) /100

P = 20 (13) / 100

P = 260 / 100

P = 2.6 Answer

2. 34th Percentile

Formula: P = 34 (n + 1) / 100

Given: 
  
k = 34 (desired size)
n = 12 (number of data we have)

Required: P34

Solution:

P = k (n + 1) / 100

P = 34 (12 + 1) /100

P = 34 (13) / 100

P = 442 / 100

P = 4.42 Answer

3. 67th Percentile

Formula: P = 67 (n + 1) / 100

Given: 
  
k = 67 (desired size)
n = 12 (number of data we have)

Required: P67

Solution:

P = k (n + 1) / 100

P = 67 (12 + 1) /100

P = 67 (13) / 100

P = 871 / 100

P = 8.71 Answer

4. 50th Percentile

Formula: P = 50 (n + 1) / 100

Given: 
  
k = 50 (desired size)
n = 12 (number of data we have)

Required: P50

Solution:

P = k (n + 1) / 100

P = 50 (12 + 1) /100

P = 50 (13) / 100

P = 650 / 100

P = 6.5 Answer

5. 25th Percentile

Formula: P = 25(n + 1) / 100

Given: 
  
k = 25 (desired size)
n = 12 (number of data we have)

Required: P25

Solution:

P = k (n + 1) / 100

P = 25 (12 + 1) /100

P = 25 (13) / 100

P = 325 / 100

P = 3.25 Answer

Solve for the following Quartiles:

(In Quartile problem, we can assign values for k from 1 - 4). But mostly, we do not solve for the 4th quartile.

1. 1st Quartile

Formula: Q = 1(n + 1) / 4

Given: 
  
k = 1 (desired size)
n = 12 (number of data we have)

Required: Q1

Solution:

Q = k (n + 1) / 4

Q = 1 (12 + 1) / 4

Q = 1 (13) / 4

Q = 13 / 4

P = 3.25 Answer

2. 2nd Quartile

Formula: Q = 2(n + 1) / 4

Given: 
  
k = 2 (desired size)
n = 12 (number of data we have)

Required: Q2

Solution:

Q = k (n + 1) / 4

Q = 2 (12 + 1) / 4

Q = 2 (13) / 4

Q = 26 / 4

P = 6.5 Answer

3. 3rd Quartile

Formula: Q = 3(n + 1) / 4

Given: 
  
k = 3 (desired size)
n = 12 (number of data we have)

Required: Q3

Solution:

Q = k (n + 1) / 4

Q = 3 (12 + 1) / 4

Q = 3 (13) / 4

Q = 39 / 4

P = 9.75 Answer

4. 4th Quartile (No need to solve usually)

Formula: Q = 4(n + 1) / 4

Given: 
  
k = 4 (desired size)
n = 12 (number of data we have)

Required: Q4

Solution:

Q = k (n + 1) / 4

Q = 4 (12 + 1) / 4

Q = 4 (13) / 4

Q = 52 / 4

Q = 13 Answer (this is by 12 + 1)

Solve for the following Deciles:

(In Decile problem, we can assign values for k from 1 - 10). In this problem, we will use only 5 problem for Decile. We will use 2nd, 4th, 5th, 7th,9th Decile. In some cases, you can use any kth decile. But mostly, we do not solve for the 10th Decile.

1. 2nd Decile

Formula: D = 2(n + 1) / 10

Given: 
  
k = 2 (desired size)
n = 12 (number of data we have)

Required: D2

Solution:

D = 2 (n + 1) / 10

D = 2 (12 + 1) / 10

D = 2 (13) / 10

D = 26 / 10

P = 2.6 Answer

2. 4th Decile

Formula: D = 4(n + 1) / 10

Given: 
  
k = 4 (desired size)
n = 12 (number of data we have)

Required: D4

Solution:

D = 4 (n + 1) / 10

D = 4 (12 + 1) / 10

D = 4 (13) / 10

D = 52 / 10

P = 5.2 Answer

3. 5th Decile

Formula: D =  5(n + 1) / 10

Given: 
  
k = 5 (desired size)
n = 12 (number of data we have)

Required: D5

Solution:

D = 5(n + 1) / 10

D = 5 (12 + 1) / 10

D = 5 (13) / 10

D = 65 / 10

P = 6.5 Answer

4. 7th Decile

Formula: D = 7(n + 1) / 10

Given: 
  
k = 7 (desired size)
n = 12 (number of data we have)

Required: D7

Solution:

D = 7(n + 1) / 10

D = 7(12 + 1) / 10

D = 7(13) / 10

D = 91 / 10

P = 9.1 Answer

5. 9th Decile

Formula: D = 9(n + 1) / 10

Given: 
  
k = 9 (desired size)
n = 12 (number of data we have)

Required: D9

Solution:

D = 9(n + 1) / 10

D = 9 (12 + 1) / 10

D = 9 (13) / 10

D = 117 / 10

P = 11.7 Answer

Question:

1. What have you noticed about the result of P50, D5, and Q2?

2. Why? 

3. How could it be?

Reply on the "Post a Comment"  Box below and we will discuss about it.

Try these yourself!

Given data:

12, 20, 19, 34, 18, 10

Solve for the following:

1. 2nd quartile

2. 50th percentile

3. 5th decile

Post your answer in the "Post a Comment"  Box below.

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HOW TO SOLVE WORDED ALGEBRAIC EXPRESSION

Tuesday, January 30, 2018

Worded Algebraic Expression

           Algebra. It is one of the mathematics' fundamental. The hard one. Majority of scholars, students, learners, find it boring, difficult and uninteresting. Algebra were always present in every school. It always appear as one of the mathematical subject form the list. You may like it or not, you need to have it to pass the semester completely. But why this subject always difficult for us?

           We always ignore every process of how system works. And our ignorance sometimes misleads us to a follow the correct flow of the system. That is why manual is always the first thing to study and not discovery as approach to know things with respect to their design. With this, comes all things difficult. We need to understand that we need a little algebraic workouts to master the Algebraic Expression as fundamental to Worded Algebraic Expression.

Let us consider this worded expression as "+" to our Algebraic expression.

Increased by
Sum
More than 
Greater than
added by
added to
Total
Plus 

Let us consider this worded expression as "-" to our Algebraic expression.

Decreased by
Diminished by
Subtracted to
Less than
Less 
Take away
Removed
Minus
Difference

Let us consider this worded expression as "x" to our Algebraic expression.

Product

Multiply

Times

Of

Twice

Let us consider this worded expression as "/" to our Algebraic expression.

Divided by

Per

Quotient of

Every

Ratio of

Split by

Let us consider this worded expression as "=" to our Algebraic expression.

is

will be

becomes

might be

will turn to

Now the worded expression to Algebraic expression

1. The sum of a and b: a + b

2. 5 added to the number: x + 5 (we can use any letter as variable to the number)

3. The quotient of x and y: x/y

4. M increased by 2: M + 2 

5. The ratio of a to b: a:b

6. Two less than a number: y - 2

7. The difference of x and y: x - y or y - x

8. 5 more than x: 5 + x

9. 7 less than x: x - 7

10. 5 times a number: 5x 

11. x divided y a number: x/y (we can use any letter as variable to the number)

12. Twice the number x: 2x

13. The product of two numbers: xy (we can use any letter as variable to the number)

14. 5 reduced by b; 5 - b

15. The sum of a number and the product of 2 and x: y + 2x

16. The quotient of two numbers subtracted from 10: 10 - x/y

17. Half of a number: 1/z

18. Nine more than twice a number: 2x + 9

19. The product of 6 and twice the number: 6(2x) 

20. Ten less than three times the number: 3z - 10

21. A number divided by 5: x/5

22. The product of a number and 5 more than the number: x + 5x 

23. The product of a number and 2 is less than a number: x - 2x

24. 5 less than a number is 7: x - 5 = 7

26. 3 less than a number is 5 more than 2 times the number: x - 3 = 2x + 5

27. Three times the sum of a number and 4 is 11: 3 (x + 4) = 11

28. Two less than four times a number is 12: 4x - 2 = 12

29: Five more than 2 times a number is one less than the number: 2x + 5 = x - 1

30. The product of 5 and a number is 8 more than twice the number less than 1: 5x = 1 -(2x + 8)


Please  make a comment in the "Post a comment" box found at the bottom and grab your copy from the link below. 

Click here for Downloadable PDF copy !!!

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MATH IS NOT A SUBJECT

Wednesday, January 17, 2018

MATH IS NOT A SUBJECT

Majority of the students from different colleges and universities find mathematics as difficult, hard, and non interesting subject. Indeed, only few loves, appreciates, embraces, and can stay the said subject easily. 

Far more than the way students handled mathematics was the another way of looking at it. Say, mathematics should not be treated as a subject but a procedural activity. Like having a new gadget which procedures from unboxing is required to use it flawlessly. Finding the gadget's switches, power buttons, etc.  was the first thing to find until we master the entire operation. Having manual for instant reading on how to how-to was sometimes ignored since we use to follow the cyber instinct that we have, and this lead us to use the said gadget limited according to its design. 

I have encountered a case about the student who was always frightened in mathematics although he loves to under go math training. He always attends seminars, tutorials, free math sessions conducted by some of their good professors in their free times at school but still he got the lowest scores every time they had math testings. He had already private tutor his parents hired to alleviate the struggle. A lots of paper scratches scattered anywhere just to justify the math solution he had from his tutor. He is not down to other subjects, in fact he always top the History, English, and other non-technical related subjects. He can't be the first honor in his class because his math hinders. He always complain that his math subject was the cause of his series of head aches, migraine and sometimes (did an intended fever) just to delay the exam schedule for mathematics. Why is this thing that happen to him happens also to some of his classmates?

Well, one of his professor one day talked and evaluate him. This professor was a doctor, a Ph.D. in mathematics. The professor conducted several different assessments. As a professional, the professor did not stop to monitor his way of studying and there it is, the professor noticed that the student study mathematics the wrong way. He, the student, opens his notebook and memorize the way his teacher did in the solution. The student follow religiously the way his teacher showing how to deal with the problem. Then the professor concluded that the reason why the student cannot understand the lesson is that student did it the way he did to English and History subjects. So the professor got an initiative how to attack this problem suffered by a child. The professor discuss about how to take care a pet (it was a dog). From puppy up to adult canine. From food proportion, water when bathing proportion, types of shampoo and soaps, time to play and walking with the dog. All consistent activity that requires how to have a healthy dog. The student can not relate the discussion of the professor, until the professor pinpointed the dog as Mathematics and the way he take care of the dog must should be the way to take care of mathematics. Every morning the dog needs food. Every morning your mathematics needs to be re-solved. The dog needs walking as exercise just like your mathematics needs to be repeat in your mind. The dog needs bathing to be clean so as your math needs accurate procedure to have clean output results and less erasures. There's a pet in your brain that needs your proper care. All of these made realization to the student that math is not a subject. It is a working and procedural activities that might lost if not cared properly. 

That is the reason why some students feel easy about math because they have mastery on it. They knew the procedures well and has a dominance dealing with it. Mathematics never change but can be lost if not be cared regularly. Everyday we must solve one mathematical problem and the mathematics will reside in your brain permanently. It develops muscle memory more than the regular memory we have. It strengthens the endurance of thinking. Improve the mental stamina, and creates good logical judgement.

MATHISNOTASUBJECT

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