NCERT Books for Class 9 Maths Chapter 14

In statistics, data are gathered, organized, analyzed, interpreted, and presented. To analyze a scientific, industrial, or social problem, it is common to start with a statistical population or model. Populations can include a wide range of people or things, such as "all individuals living in a country" or "every atom in a solid." Statistics involves planning data collection methods, such as surveying and doing experiments. Mathematics is applied to statistics in a process known as mathematical statistics. Mathematics tools used in this process include analysis, linear algebra, stochastic analysis, differential equations, and measure-theoretic probability theory.

With the development of probability theory by Gerolamo Cardano, Blaise Pascal, and Pierre de Fermat in the 17th century, the mathematical underpinnings of contemporary statistics were created. Although the idea of probability was already addressed in medieval law and by philosophers such as Juan Caramuel, mathematical probability theory originated from the study of games of chance. Adrien-Marie Legendre was the first to describe the least-squares approach in 1805.

Statistical approaches are now used in all sectors that need decision-making, for producing reliable inferences from a large body of data, and for making conclusions based on statistical methodology in the face of ambiguity. Modern computers have sped up large-scale statistical computations and enabled novel procedures that would be impossible to accomplish manually. Statistics is still a hot topic of study, as evidenced by the issue of analysing large amounts of data.

Overview of the Chapter

1. Introduction

We come across a lot of data every day in the form of facts, numerical figures, tables, graphs, and so on. Newspapers, TV, periodicals, and other forms of communication supply these. These may include batting or bowling averages in cricket, corporate revenues, city temperatures, spending in various areas of a five-year plan, polling results, and so on. Data refers to numerical or non-numerical facts or statistics collected for a certain reason. The plural version of the Latin word datum is data. Of course, you're not unfamiliar with the term "data." In previous classes, you learned about data and how to handle it. Our world is becoming increasingly information-centric. The use of data is everywhere and in everything today. As a result, knowing how to extract useful information from such data becomes critical. Statistics is a discipline of mathematics that studies the extraction of useful data. The word statistics is said to have sprung from the Latin word status, which means a (political) state. Statistics began as a simple gathering of data on many elements of people's lives that the government might exploit. However, statistics' scope grew throughout time, and it began to concern itself not just with the collecting and display of data, but also with the interpretation and inferences drawn from the data. Statistics is the study of data gathering, organisation, analysis, and interpretation. In different settings, the term "statistics" has distinct connotations.

2. Collection of Data

Data collection in statistics is the process of obtaining information from all relevant sources to solve a research topic. It aids in the evaluation of the problem's outcome. The data collecting methods enable a person to conclude Upper-class the relevant question. Methods for collecting primary data.

3. Presentation of Data

The information gathered might be presented in a tabular, diagrammatic, or visual format. A table is a column-by-column and row-by-row arrangement of categorised data. When an experiment has a significant number of observations, the number of times a value appears in the data is tabulated, which is known as the frequency of that value. A frequency distribution table is a table that depicts the frequency of distinct values in a set of data. An ungrouped frequency distribution table is a frequency distribution table that indicates the frequency of each unique value in the provided data. A grouped frequency distribution table is a table that displays the frequency of groupings of values in a set of data. Classes or class intervals are the groups used to group the values in provided data. The class size or class width refers to the number of values included in each class.

4. Graphical Representation of Data

The use of tables to represent data has already been considered. This section looks at another type of data representation, namely the graphical representation. According to the saying, a picture is worth a thousand words. When comparing things, graphs are usually the easiest way. The depiction becomes more understandable than the facts themselves. In this part, we'll look at the graphical representations that follow.

1. Bar graphs 

2. Histograms of uniform width and varying widths

3. Frequency polygons 

5. Measures of Central Tendency

It portrayed the data in a variety of ways earlier in this chapter, including frequency distribution tables, bar graphs, histograms, and frequency polygons. Now the question is whether we always need to analyse all of the data to make sense of it, or if we can extract some key aspects by looking at only a few representative samples. Using measurements of central tendency or averages is achievable.

Important Terms 

• Ungrouped Data: Ungrouped data is data in its unprocessed or unaltered state.

• Grouped Data: In grouped data, all of the observations are placed into a single group.

• Frequency: The total number of times a certain piece of information or observation appears in the data.

• Class Interval: All of the data in a chart can be separated into groups or class intervals, with all of the observations in that range belonging to only that group.

• Class Width: Upper-class limit - lower class limit

• Mean: The average of "n" numbers is found by dividing the sum of all the numbers by n.

• Mode: It is by far the most common observation. In a class interval, the modal class is the one with the highest frequency.

• Median: The median is the value of observation in the centre.