Statistics & Probability

Welcome to the *astoundingly clear introduction* to statistics and probability. Learn in this

• how data can be organized in tally and table form

• how data collected in statistics can be used to *predict future* occurrences

• how the predicting the outcome can be captured as a *probability in random experiments*. The details are *ingenious and provided nowhere else*.

• how continuous data can be represented as grouped data and analyzed

Understanding Statistics

A simple introduction to what is data and what we learn in statistics is given with an example.

Tally and Table Representation of Data

With examples, the tally and table representations are introduced.

Pictograph representation

With simple examples, the pictograph representation of Data is explained.

Bar-graph representation

With simple examples, the bar-graph representation of Data is explained.

Cumulative Frequency

In this page, the following are introduced with examples

• range of data

• frequency of a data-point

• cumulative frequency

Representative Values of Data : Mean, Median, Mode

In this page, the mean, median, mode of a data is introduced with examples.

• Mean is the value when the data is evenly distributed to all the values.

• Median is the value that has equal number of smaller and larger data values in the given data.

• Mode is the value that is repeated most number of times in the data.

Central Tendencies of Data : Mean, Median, Mode

In this page, computing mean, median, and mode using tally / table form of data is explained with examples.

Bar-graphs : Representation and Reading

In this page the following are covered.

• Reading a bar-graph of given data

• Representation of two sets of data using bar-graphs

• Representation of data using pie-charts

Statistics to Predict Future

Learn how data collected can be used to * predict future*. This is an important lesson, and it is not found in any other books or websites.

Introduction to Random Experiments

The following are introduced and explained

• random experiment

• possible outcomes

• sample space

• sample point

• event

• probability of an event

Probability of an Event in Random Experiments

In this page, learn how statistical data can be used to predict an outcome of a random experiment.

Such prediction requires large effort and small variations in the data can cause errors.

So the possible outcomes are theorized as having equal chances and the probability of an outcome is defined.

Standard Random Experiments

The following standard random experiments are explained.

• tossing a coin

• rolling a dice

• picking a ball of a color from a box

In each of these, the statistical methods to predict the outcome of an experiment requires large effort and small variations in data can cause errors in the prediction. So the possible outcomes are theorized as having equal chances and the probability of an outcome is defined.

Introduction to Grouped Data

Grouped data is introduced and explained with some examples.

Predicting using Grouped Data : Probability

In this page, finding probability of grouped data is explained with some examples.

Grouped Data - Class Interval & Class Mark

In this page, class interval and class mark of grouped data is explained with some examples.

Mean of Group Data - Direct Method

In this page, finding mean of grouped data is explained with some examples.

Simplified procedures to find mean are explained.

(a) assumed mean method,

(b) step deviation method

Mode of Group Data

In this page, finding mode of grouped data is explained with some examples.

The formula is derived for students to understand how mode is calculated -- this is not available in other books.

Median of Group Data

In this page, finding median of grouped data is explained with some examples.