interquartiles

Hello students, in this session we are going to discuss the interquartiles and How to Find the Interquartile Range. The interquartiles come under the quartiles and the quartiles are one of the types of partition values. The other two types of partition values are deciles and percentiles. Quartiles defines the whole series into four equal parts and these four equal parts are denoted by the Q₁, Q₂, Q₃ statistics where Q₁ contains first 25 % data of whole data and known as lower quartile, Q₂ contains 50 % data of whole data and known as median and Q₃ contains last 25 % data of whole data and known as upper quartile. So the interquartile is the statistics range between the Q₃ and Q₁ or in other words interquartile range is Q₃ - Q₁.
By subtracting the lower quartile from the upper quartile we can find the interquartile value. Another formula to find the interquartile i9s Range = X _{max –} X _min, Where X _max is upper observation and X _min is lower observations.
Interquartiles statistics is used for the quality control of those products that are manufactured. We can also find the semi interquartile range, so formula for this is : - (Q₃ - Q₁) / 2
Let’s take an example of interquartile range
We have a data series 1, 3, 5, 96, 78, 4, 52
Step 1 : - First of all arrange this series into ascending order
1, 3, 4, 5, 52, 78, 96
Step 2 : - Find median (median is always middle value)
So the median is 5.
Step 3 : - Put the numbers into parentheses
(1, 3, 4) 5, (52, 78, 96)
Step 4 : -After got the median we have to find Q₁ and Q₃
Q₁ is just half of the lower side data, so it is 3
Q₂ is just half of the upper side data, so it is 78
Step 5 : - Now subtract Q₃ – Q₁ to find interquartile range.
78 – 3 = 75

In upcoming posts we will discuss about Discrete and continuous random variables and Basic trigonometric functions. Visit our website for information on Maharashtra secondary and higher secondary education board

Permutations and combinations

In every area we use Permutations and combinations which are the part of Algebra 2, but generally the permutations and combinations are use in mathematics filed. They are the fundamental principles of counting. The main difference between the permutations and combinations according to board of secondary education Andhra Pradesh is, when the orders means a lot then it is said to be permutations and if the order means nothing then it is said to be combinations. Just take examples for both: -
A permutation is also an ordered combination. Permutations are of two types: -
-Repetition is allowed.
-No repetition.
Example of Permutations: - If the 893 is the password combination of any id then it cannot be 398. Because to apply the 398 we cannot open the id, to open the id we have to insert the 8-9-3 in exact order. In this order matters alot.
Combination is also two types: -
-Repetition is allowed.
-No repetition
Example of Combination:- If I am saying that my vegetable salad is a combination of onions, tomatoes and chilies, then the order means nothing to us, we do not take care the order, either they could be in order like onions, tomatoes and chilies or chilies, tomatoes and onions. It will be same vegetarian salad. No matters what is the order.
Permutations and combinations formula,
Permutations formula for repetition: -n ^r.
Permutations formula without repetition: - n ! / (n –r) !,
Combination formula for repetition : - (n + r – 1) / r = (n + r – 1) ! / r ! (n – 1) !,
Permutations formula without repetition: - n ! / r ! (n – r) ! = (n / r),
By applying the above formulas we can solve the any type of permutations and combination problems.


In upcoming posts we will discuss about Measures of central tendency and Geometric proofs in Grade XII. Visit our website for information on Ogive

Permutations and combinations

Hi friends, we are discussing the topic Permutations and combinations of ssc board Andhra Pradesh in this blog. The combinations and permutations are part of algebra which is part of Discrete math.  In combination the order of things is not important, example: the fruit salad is combination of papaya, mango, grapes, apple we do not care what order of fruits is in.
The combination is two types: 1) repetition 2) not repetition.
Allowed the Repetition: in your pocket the number of coins can be repeated (2, 2, 2, 5, 5, 10, 10)
Repetition is not allowed: in the lottery numbers repetition is not allowed (5, 67, 45, 96, 24, 54)
Example of the combination: when we are choosing balls the possibilities of selection can be 1, 2, 3 balls.
Order does matter: 123, 132, 231, 321, 312, 213. The formula of combination is ^aC_b
            a!               (! this symbol is used for the factorial operation)
^aC_b =---------
       b!(a-b)!      
Here, a is the number of things from which we have to choose b number of things.
The formula is applied on example where we have to choose 3 out of 5 different balls:
   5!                5!             120
 ----------- = ---------  =  10 ways of combination.
  3!(5-3)!     3!*2!            12
Permutation is an order of combination in which the order does not change (visit for more information on permutation). The lock is the best example of permutation; the permutation is totally different to the combination. Permutations are basically of two types:

1.      Repetition is compulsory: the code of the lock is: 555. The repetition is allowed in this case and order does not matter.

Simple formula for repetition: a^b
Here a*a*a*.........(b times)=a^b

2.      No repetition allowed: In this we have to reduce number of available choices for each time

Example: in the pool game number of balls is fixed. One ball is used one time and no repetition is allowed for using the same ball. The formula of no repetition permutation:
            a!         (!- this symbol is used for the factorial operation)
 ^aP_b=-------
         (a-b)!
An Example of this permutation can be when we have to pick 2 out of 5 balls in all possible ways:
5!           5*4*3*2*1      120
---- – = ---------- ---- = 20 ways
(5-2)!        3*2*1          6


In upcoming posts we will discuss about Math Blog on Grade XI and Properties of quadrilaterals. Visit our website for information on How to Calculate Standard Deviation