Key Points

Data is a collection of information, usually facts or numbers, gathered for a specific purpose or study. For example, the number of runs scored by a cricketer in different matches is data.

Data can be represented visually using graphs like pictographs, bar graphs, double bar graphs, and pie charts. This makes the information easier to understand and interpret at a glance.

A bar graph uses rectangular bars of uniform width to represent data. The height or length of each bar is proportional to the value of the data item it represents, making it useful for comparing quantities across different categories.

A double bar graph is used to display and compare two sets of related data simultaneously. For instance, it can be used to compare the marks of students in two different academic years.

A pie chart, also known as a circle graph, shows the relationship between a whole and its parts. The entire circle represents the total value, and the different sectors of the circle represent the proportion of each part.

To draw a pie chart, the central angle for each sector is calculated. The formula is: Central Angle $= \frac{\text{Value of the component}}{\text{Total value}} \times 360^\circ$. The sum of all central angles in a pie chart must be $360^\circ$.

A random experiment is an action or process for which the outcome cannot be predicted with certainty, even if it is repeated under the same conditions. Tossing a coin or rolling a die are examples of random experiments.

An outcome is a possible result of a random experiment. An event is a specific outcome or a collection of outcomes. For example, when rolling a die, getting a '4' is an outcome, while getting an 'even number' (2, 4, or 6) is an event.

Outcomes of an experiment are considered equally likely if each outcome has the same chance of occurring. For example, when a fair coin is tossed, the outcomes 'Head' and 'Tail' are equally likely.

Probability is the measure of how likely an event is to occur. For equally likely outcomes, the formula is $P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$.

The probability of any event always lies between 0 and 1, inclusive. A probability of 0 means the event is impossible, and a probability of 1 means the event is certain. This is expressed as $0 \leq P(\text{Event}) \leq 1$.

When a single fair die is thrown, there are 6 total outcomes {1, 2, 3, 4, 5, 6}. The probability of getting a number greater than 4 is $P(\text{number} > 4) = \frac{2}{6} = \frac{1}{3}$, as there are two favorable outcomes (5 and 6).