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

quartiles

Hello students, in this session we are going to discuss the quartiles from Gujarat secondary education board. Quartiles are the partition values. They are the same like the mean and median, mean, median divides the whole series into some equal parts and partition values also divides the series into certain equal parts. Besides quartiles, there are also two methods, such as deciles and percentiles. But here we have to discuss the quartiles (for more information visit here).
The quartile definition: - quartiles separate the whole series into 4 equal parts. And the four equal parts are denoted by the 3 quartiles. Four equal parts means 25%, 25% 25%, 25% and the quartiles can be represented by Q,
Q1 = first quartile called the lower quartile and have first 25% of data.
Q2 = second quartile called the median and have 50% of data.
Q3 = first quartile called the upper quartile and have last 25% of data.
Note: - To define the quartiles we have to first arrange the data into ascending order
Let’s take an example.
We have data set 8, 7, 87, 34, 78, 5, 65, 67, 23, 9, 11
Solution: - First of all we have to sort this data 5, 7, 8, 9, 11, 23, 34, 65, 67, 78, 87
Q1 = 8
Q2 = 23
Q3 = 67
We can also follow the formulas to obtain Q1, Q2 and Q3,
Quartiles in individual series
Q1 = (n+1^th )/4 item
Q2 = (n+1^th) /2 item
Q3 =3 (n+1^th) /4 item
Quartiles in Discrete series
Q1 = size of (n+1^th )/4 item
Q2 = size of (n+1^th) /2 item
Q3 =size of 3 (n+1^th) /4 item
We can also calculate the Q1, Q2 and Q3 for the continuous series by applying their formulas

In upcoming posts we will discuss about dispersion and Learn factoring of Two Degree Polynomials. Visit our website for information on Binomial Probability Distribution