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Data

Introduction

Data are characteristics or information, usually numerical, that are collected through observation. Data can be either qualitative or quantitative.

Measures of Central Tendency

When describing a set of data, the central position of the data set is identified. This is known as the central measure of tendency. The three most common measures of central tendency are mean, median and mode.

Mean

Mean is the most common central tendency we know about and use. It is also known as average. It is simply the sum of all the items in a list or collection, divided by the number of items.

Example:

example of calculating mean of given list of numbers

Learn the formula used to calculate the Mean for a given set of data.

Median

The median is the middle value of a set of numbers arranged in increasing order.

Example:

example of calculating median of given list of numbers

For finding the median, it is necessary to write the components of the group in increasing order.

Mode

In any collection of numbers, the number which occurs the most number of times is the mode.

Example:

example of calculating mode of given list of numbers

To calculate the mode in the case of grouped frequency distribution, we first identify the modal class, the class that has the highest frequency. Then, we will use the formula given to calculate the mode.

Data Handling

Data Handling refers to the process of gathering, recording and presenting information in a way that is helpful to others. Data is usually represented in the form of pictographs, bar graphs, pie charts, histograms, line graphs, etc.

Example:

Pictograph used for data handling

example of how to read a pictograph

Pie chart used for data handling

example of how to read a pie chart

Bar graph used for data handling

example of how to read a bar graph

Line graph used for data handling

example of how to read a line graph

Histogram used for data handling

example of how to read a histogram

Data Handling is a very important concept when it comes to statistics. It helps us to store and present the results from any research conducted. In schools, you too might have undertaken tasks in which teachers encourage students to collect data about yourselves, your friends, family, surroundings and more. The purpose of data handling is to present data in a variety of forms such as Pictographs, Bar Graphs, Pie Charts, Histograms, and Line Graphs.

Probability

Probability means how likely it is for a random event to occur. Its value is expressed between \(0\) and \(1.\)

Example:

possible outcome achieved by rolling a dice

Many times we are not sure about the outcomes of certain events. In those cases, we try to measure the likelihood of the occurrence of such outcomes. In Probability, you will get to learn how to calculate the number of possible outcomes that are likely to occur for events like Tossing a Coin, Rolling a Die, and Drawing a Card. You will also be familiarised with the Terminology of Probability.

Permutations and Combinations

A combination is a way of choosing elements from a set in such a way that the order does not matter.

A permutation is an act of arranging the elements of a set into a sequence or order.

Example:

example of permutation and combination concept

Permutations and Combination is a way of selecting and representing a particular data or object. To understand permutations and combinations better we first start off with Practical Counting Situations and Examples on Practical Counting Situations. You will then get to learn more about permutations with the help of Examples for Permutations as Arrangements. Similarly, in the case of combinations, you can refer to the Examples of Combinations as Selections, for a better understanding of these concepts.