In statistics, the central tendency reflects the centre of the data distribution. Generally, the central tendency of a dataset can be defined using some of the measures in statistics known as measures of central tendency.
Basic concepts of Set Theory like Union, Intersection, Complement of a Set, etc have significant use in Algebra, Logic, Combinatorics, probability, etc. Therefore, this topic is of grave importance in Banking and MBA exams.
On that note, let’s discuss both of these concepts in-depth so that you can use them to ace any Sets and Statistics questions in any competitive exam.
Measures of Central Tendency
The three important measures of mean, median, and mode can be used to find the dataset’s central tendency.
Mean
The average value of the dataset is represented by the mean. The sum of all the values in the dataset divided by the number of values can be determined. It is commonly referred to as the arithmetic mean.
Geometric Mean, Harmonic Mean and Weighted Mean are different mean measures
The following is the formula for calculating the mean value:
Sum of values of all observations/number of observation
Median
The median is the dataset’s middle value, whether the dataset is sorted in ascending or descending order.
Consider a case of odd number of observations arranged in descending order – 23, 21, 18, 16, 15, 13, 12, 10, 9, 7, 6, 5, and 2
The number 12 is the median number.
Consider a case of even number of observations in descending order – 40, 38, 35, 33, 32, 30, 29, 27, 26, 24, 23, 22, 19, and 17
The two middle values of the given dataset are 27 and 29.
Now calculate the average of these two figures.
i.e.,(27+29)/2 =28
As a result, the given data distribution’s median is 28.
Mode
The mode represents the value that appears most frequently in the dataset. There are instances when the dataset has many modes and other times when it does not.
Consider the following numbers: 5, 4, 2, 3, 2, 1, 5, 4, 5.
The most often occurring value in the sample is 5.
Sets
Sets are represented as a collection of well-defined objects or elements and it does not change from person to person. A set is represented by a capital letter.
They can be expressed in set-builder or roster form. Curly braces are commonly used to represent sets; for example, A = {1,2,3,4} is a set.
Types of Sets
We have several types of sets in Maths. They are empty sets, finite and infinite sets, equal sets, Disjoint Sets, Subsets, Supersets, Universals sets and so on.
Operations on Sets
The basic operations on sets are:
Union of Sets
If two sets A and B exist, A union B is the set that contains all of the elements of both sets. It’s written as A B.
For instance, if A = {1,2,3} and B = {4,5,6} then A union B is:
A ∪ B = {1,2,3,4,5,6}
Intersection of Sets
If sets A and B are two sets, then A intersection B is the set that only contains the elements that are shared by both sets. It’s written as A B.
If A = {1,2,3} and B = {4,5,6} the A intersection B is as follows:
A ∩ B = { } or Ă˜
Because A and B share no elements, their intersection will result in a null set.
Complement of Sets
The complement of any set, such as P, is the collection of all items in the universal set that aren’t in set P. P’ is the symbol for it.
Double complement law: (P′)′ = P
Cartesian Product of sets
If sets A and B are two sets, then their cartesian product is a set containing all ordered pairs (a,b) in which an is an element of A and b is an element of B. A.B is the symbol for it.
Example: set A = {1,2,3} and set B = {Bat, Ball}, then;
A Ă— B = {(1,Bat),(1,Ball),(2,Bat),(2,Ball),(3,Bat),(3,Ball)}