### Averages:

Average is a number that represents or shows the central tendency of a group of observations of data.

### Arithmetic Mean and Range

The **average **or arithmetic mean or **mean** of a given data is defined as :

Mean=Sum of all observations / Number of observations

The **difference **between the **highest** and the **lowest** observations in a given data is called its **Range**.

Example: Ages of all 10 teachers in grade 7 are : 25, 43, 34, 55, 44, 60, 32, 29, 35, 40.

Mean = 43+34+55+44+60,+32+29+35+40 = 39.7 years

Range = Higest Observation – Lowest Observation = 60 – 25 = 35

### Median

When a given data is arranged in ascending (or descending) order, then the middlemost observation is called the median of the data.

Example : Marks scored by seven students in a class are: 21, 32, 18 ,93, 21, 36, 50.

Observations in ascending order: 18, 21, 21, 32, 36, 50, 93.

Middle most value = 32

∴ Median is 32.

### Mode

The **mode** of a set of observations is the **observation that occurs most often**.

Example: Given set of numbers: 1, 1, 2, 4, 3, 2, 1, 2, 2, 4

Ascending Order = 1, 1, 1, 2, 2, 2, 2, 3, 4, 4

∴ Mode of this data is 2 because it occurs more frequently.

**Note**: A data can have more than 1 mode.

## Probability

**Probability** is the **measure** or the **chance of occurrence** of a particular event. Experiments which do not have a **fixed result** are known as **random experiments.**

**Number of outcomes or Sample Space ** The set of **all the possible outcomes** to occur in any experiment is known as **sample space.
**

**Examples:**Experiment : Tossing a coin, Sample Space (S) = {H,T}

Experiment : Rolling a die, Sample Space (S) = {1,2,3,4,5,6}

**Favourable outcome –** It is one of the possible result(s) of an experiment.

### Double Bar Graphs

**Double bar graphs** are an effective tool to **compare** the values of **two quantities for the same observation**. For example, consider the marks obtained by five students of a class in two tests. Using a double bar graph, we can analyse which week students had better marks.

NCERT Solutions