[Maths Class Notes] on Data Sets Pdf for Exam

What is a Data Set?

Dataset meaning corresponds to the collection of data that is similar. A data set is generally represented in the form of a table. In this table, each column corresponds to a variable and each row corresponds to the values of the variable whose data is collected. Datasets find a huge range of applications in the comparison, prediction, or computation involved in several domains of Statistics, Economics, Mathematics, and Science. The datasets consist of past, present, and future data which can be used for comparisons.

Data Set Meaning:

Handling the large data in various domains of the real-world is a tedious task. It needs the utmost care in the collection, classification, arrangement, and storage of data. Each datum should be classified carefully so that it can be easily fetched when the access is required. The data is therefore arranged in an organized manner in the form of tables or schematic symbols or any other Mathematical objects so that they can be easily accessed when required. This kind of data arranged in a specified pattern is called the data set. 

To understand the data set meaning, let us consider an example of a school. The marks of a student in Class 9 in one of the unit tests conducted in the month of July 1999 is to be rechecked in a school consisting of 3500 students in a year. In this case, the data of marks obtained by the students is classified under different types of data sets like year-wise, class-wise, month-wise, subject wise, etc. This organized arrangement of the data of student’s marks helps the management of the school to fetch the marks easily in a short time. However, if the data is haphazard fetching of the data when required becomes highly complicated.

Sample Data Sets:

Sample data sets are the data sets obtained from a specified statistical population. The process involved in collecting the sample data sets is called the sampling. Any scientific study or research is performed over a set of sample data before it is generalized. For example research is made that a particular medicine is newly invented which is capable of curing cancer. Before this medicine is set out in the market, the medicine is first tested on a few sample data sets such as a sample of rats, a sample of higher animals, and finally the sample data sets of human beings. If the research succeeds with a positive result in all the sample data sets, then it is generalized and released for public use.

Types of Data Sets:

The different types of data sets are:

Numerical data set example: Height and weight of a people, the population of a country, a score of students, etc

Example: Age and systolic blood pressure of a group of people

• Multivariate datasets: The data set consists of data values of more than two variables.

• Categorical datasets: The datasets which represent the specific category of data based on their characteristics are called categorical datasets.

Categorical data set Example: Gender of an animal, state of matter of a substance, etc.

Example: The height and weight of a group of people are interdependent with each other. 

Measures of Central Tendency of Data sets:

Central tendency is a measure of the central value of the collected data in a dataset. There are three measures of central tendency. They are:

1. Mean: It is the average value of all the samples of the given dataset.

2. Median: It is the middle value or midpoint of the values in the sample data sets.

3. Mode: It is the most repeated value in the given sample datasets. 

Data Set Example Problem:

1. The sample values of data in a data set example are given in the table below. Find the mean, median and mode of the given values in the data set.

[7, 9, 4, 7, 6, 4, 3, 1, 7, 7]

Solution:

Values of dataset arranged in ascending order = [1, 3, 4, 4, 6, 7, 7, 7, 7, 9]

Mean of the given dataset is its average

Mean = [frac{Sum of Values}{No. of Values}] = [frac{7+9+4+7+6+4+3+1+7+7}{10}] = [frac{55}{10}] = 5.5

Median is the middle value of the data set. Since the data set consists of 10 values,

Median = [frac{6+7}{2}] = [frac{13}{2}] = 6.5

Mode of a given dataset is the most repeated value in the dataset.

In the given dataset, the value ‘7’ is repeated the maximum number of times.

Mode = 7

Fun Facts about What is Data Set:

• If a data set does not contain any missing values or any aberrate data and can be easily altered, then such a dataset can be regarded as a good dataset.

• Datasets form the basic building blocks of various domains of data mining and data science.

• Central tendency measurements are applicable only for numerical datasets.

• Range of a dataset is the difference between the highest and lowest values in the dataset.