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Maths Query > Unit > Statistics > Data Handling

# Data Handling, Presentation and Interpretation

## Introduction

What is data, information and how the data is collected and organized to get a good piece of information are introduced in as simple as possible in this chapter Data Collection and Organization.

In statistics, data handling is a way of collecting, organising, presenting the data on charts or graphs and how to read and interpret the graphs. After data collection, data is organised using tables.

Data can be represented in different ways such as pictograph, bar graph, line graph, histogram, tables, tally charts etc.

AS we already know the ways of collecting and organising the data, now we move on to presenting them on graphs and charts.

## Presentation of data

Once the data is organised into a table, that will be ready for the presentation on charts and graphs. The benefit of presenting the data into charts and graphs is that the data can be visually compared better than the tables.
Below are the types of graphs and charts that are used commonly like pictograph, bar graph, double bar graph, histogram, pie charts and line graphs. Let’s have a look next at them with examples.

## Pictograph

In pictographs data is represented using pictures or symbols, it is called pictograph. A picture or a symbol is selected for a value then it is plotted on graphs.

Let’s see how to make a pictograph of information of students who like table tennis, football, cricket, hockey and volleyball.

Table: Data of games liked by students

GamesNumber of students
Table tennis5
Football7
Cricket3
Volleyball6

This information of students who like table tennis, football, cricket, hockey and volleyball can be presented in the form of pictures. So, let’s make a pictograph for this.

### How to draw Pictograph?

GamesNumber of students
Table tennisπ π π π π
Footballπ π π π π π π
Cricketπ π π
Volleyballπ π π π π π

Here, π is the picture that is selected to represent 1 student.
There are 5 students who plays table tennis games, so its entry in the graph will have five number of π in the above pictograph.
Similarly, students playing football, cricket, volleyball and basketball will have 7, 3, 6 and 2 π pictures respectively on the pictograph.

### Interpretation of pictograph

By observing the above pictograph, we can interpret the following information

1. Football is liked by maximum number of students.
2. Basketball is liked by minimum number of students.

## Bar graph (Column graph)

Bar graphs are also known as bar charts or column graphs. Bar graph uses bars to represent the data. These bars can be in a vertical or horizontal position.

### Types of bar graph

Depending upon the position of bar in bar graph, it is of two types vertical bar graph and horizontal bar graph.

1. Vertical bar graph
2. Horizontal bar graph

#### 1. Vertical bar graph

The bar graph which have vertical bars is called a vertical bar chart.

#### 2. Horizontal bar graph

The bar graph which has horizontal bars is called a horizontal bar chart.

Let’s draw horizontal and vertical var graphs from the following data of number of items sold in a day.

Table: Data of number of items sold in a day

DaysNumber of items sold
Sunday10
Monday15
Tuesday20
Wednesday10
Thursday40
Friday45
Saturday30

### Steps to draw bar graph

1. Draw two perpendicular lines, i.e. one vertical and other is horizontal. These perpendicular lines are called vertical axis and horizontal axis also. These both axis will represent the data that from the table that needs to be drawn on the graph.
2. Mark the vertical and horizontal axis by names from the table column names.
3. Draw bars for each observation from the table and keep all bars in a graph of the same width always. The gap between two bars should always be kept the same.
4. Choose suitable scale along vertical line.

These steps work to draw both types of bar graphs vertical and horizontal.

Some important things to keep in mind while making a bar graph are: The width of all bars in a bar graph are kept the same.
The space between all bars in a graph must be equal.
The height of each bar represents the numerical value of data.

So, let’s see next how to draw a bar graph using the following table which has the sale of different items sold at a grocery shop on different days.

### Interpretation of bar graphs

1. The bar graph gives information of number of items from sunday to saturday.
2. The maximum number of items sold on friday.
3. The minimum number of items sold on sunday and wednesday.

## Double bar graph

As the name suggests, double bar graphs have two bars on the graph unlike a bar graph, which has only one bar. The purpose of two bars in a double bar graph is to make comparison between two sets of data.

Steps to make a double graph are all the same as a bar graph. The only difference lies in the number of bars. Double bar graphs will use two bars from two columns of numerical data from a table.

Consider the following table having data of number of items sold by a shop on two different days saturday and sunday. First column has the name of the item. Second and third columns keep the number of items sold on saturday and sunday.

Table: Number of items sold on saturday and sunday

Name of itemNumber of items sold on saturdayNumber of items sold on sunday
Shirts1020
Pants3020
Socks4030
Ties3070
Belts2060

This type of data where there are two columns of numerical data can be best represented using a double bar graph.

### Interpretation of double bar graph

1. Maximum sale is on sunday for ties.
2. Minimum sale is on saturday for shirts.
3. Sale of shirts on sunday is more than on saturday.
4. Sale of pants on saturday is more than on sunday.
5. Sale of socks on saturday is more than on sunday.
6. Sale of ties on sunday is more than on saturday.
7. Sale of belts on sunday is more than on saturday.
8. Sale of shirts, pants and belts are sold equally.
9. On sunday shirts and pants are sold equally.

## Histogram

Histogram is another graphical representation of frequency distribution. Histogram shows the data in intervals such that there is no gap between any bars. It means it has adjacent bars over the intervals. It has bars with class intervals as bars and heights proportional to corresponding frequencies.

The information data can be presented in the form of histogram.
To draw histogram, we need to follow some steps.

The following table shows the marks scored by students in examinations.

MarksNumber of students
0 – 105
10 – 2010
20 – 3015
30 – 4020
40 – 5025
50 – 605

### Steps to draw histogram

1. Draw one horizontal line and the vertical line.
2. Take horizontal line as x-axis and mark it as class internal.
3. Take vertical line as y-axis and mark it as frequencies.
4. Construct bars with class interval as bars and respective frequencies as heights.

### Interpretation of histogram

By observing the graph, we can analyse that

1. Number of students are same who scored the marks between 0 to 10 and 50 to 60.
2. Maximum number of students scored the marks between 40 to 50.

## Pie Graph or Pie Chart

Pie graph is also a pictorial representation of numerical data, represented by sectors of circle.
A pie graph is used to compare parts of a whole and the circle represents the whole.
The circle is divided into as many sectors as there are quantities of data. The area of each sector is proportional to the quantity it represents.

### Steps to draw pie graph

1. From the given data, find the sum of all given quantities.
2. Divide each given quantity by the sum obtained in step 1 and multiply it by 3600 to get the value of a sector angle or central angle.
3. Draw a circle of any radius.
4. Construct the various sectors corresponding to its central angle in clockwise direction.
5. Put explanatory or descriptive labels inside each sector.

To construct the pie graph, we need to find a central angle corresponding to a given quantity, which is calculated using this formula.

Formula

Central angle = $\frac{value of given quantity}{sum of all given quantities}$ × 360

### Draw pie chart

The following data shows the expenditure of a person on different items during a month.

Table: Data of expenditure of different items in a month

Items of expenditureAmount spent
Food300
Rent400
Clothing150
Education250
Miscellaneous100

From the above table calculate the central angle for each of the item.

Table: Data of expenditure of different items in a month with calculated central angle

Items of expenditureAmount spentCentral angle
Food300 $\frac{300}{1200}$ × 360 = 90°
Rent400 $\frac{400}{1200}$ × 360 = 120°
Clothing150 $\frac{150}{1200}$ = 45°
Education250 $\frac{250}{1200}$ = 75°
Miscellaneous100 $\frac{100}{1200}$ = 30°

Now, follow the following steps to draw the pie chart of expenditure of different items in a month.

1. Draw a circle of any radius.
3. Construct a sector of central angle of 900 starting from the radius drawn in the above step in clockwise or anticlockwise direction.
4. Draw other sectors of central angle 1200, 450, 750 and 300.
5. Shade all six sectors by different colors and label them.

Pie chart

### Interpretation of pie chart

1. Maximum amount has been spent on item rent.
2. The least amount was spent on item miscellaneous.

## Line graph

Line chart or line graph is known as curve chart. Line graph displays the data that changes continuously over periods of time. In this chart, data displays a series of data points which are called as markers. There data points are connected by time segments. A time chart is used to analyse the travel in data over specific interval of time.

The given data shows the January temperature on different days in the city.

Table: January temperature on different days

DateMaximum temperature
114°
210°
3
4
510°
612°

### Steps to draw line chart

1. To draw a line chart, we take two axes x-axis and y-axis.
2. On the x-axis, we represent dates of month and on the y-axis we represent temperature.
3. We plot the ordered points (1, 14), (2, 10),(3, 8),(4, 6),(5, 10) and (6, 12) as points.
4. Then we join these points by line segment.

### Interpretation of line graph

1. The minimum temperature was recorded on December 4.
2. On December 2 and December 5, the temperature was same as 100C
Last updated on: 27-07-2024