#### अध्याय 3: आँकड़ो का प्रबंधन Class 7 Math

## Data Handling Class 7 Notes: Chapter 3

## 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.

## Averages

### 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.

## Chance and 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.**Examples :** In an experiment of Tossing a coin, getting a head. Favourable outcome = {H} In an experiment of Rolling a die, getting an even number Favourable outcomes = {2,4,6} Probability of occurrence of any event,

P(E)=Number of favourable outcomes / Total Number of Outcomes

Example: Find the probability of getting an even number when a die is rolled. Sample Space (S) = {1,2,3,4,5,6} , Favourable outcomes = {2,4,6} P(E)=Number of favourable outcomes / Total Number of Outcomes =3/6=1/2

## The Scale

Large numbers cannot be represented in a bar graph, so the

scaling factoris used toreduceor scale downlarge numbers.## Organization of Data

Data is

organisedandrepresented graphicallyso that it becomes easy to understand andinterpret. This is called anorganisation of data.## Pictographs and Bar Graphs

A pictographis apictorial representationof data. Here data is represented using images of the objects.The graphical representation of data using

bars of uniform width drawn vertically or horizontallywith different lengths is called asbar graphs/bar diagrams.Bar diagrams consist of two axes: X-axis and Y-axis. The following is a bar graph showing the birthday of students in a class. Graph showing the birthday of students in a class.