MATHS
QUERY

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.

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.

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.

Example

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

**Table 1: Games liked by students **

Games | Number of students |
---|---|

Table tennis | 5 |

Football | 7 |

Cricket | 3 |

Volleyball | 6 |

Basketball | 2 |

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.

**Table 2: Pictograph**

Games | Number of students |
---|---|

Table tennis | π π π π π |

Football | π π π π π π π |

Cricket | π π π |

Volleyball | π π π π π π |

Basketball | 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 above pictograph**

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

- Football is liked by maximum number of students.
- Basketball is liked by minimum number of students.

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.

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

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

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

- 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.
- Mark the vertical and horizontal axis by names from the table column names.
- 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.
- 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.

Example

**Table 3: Number of items sold in a day**

Days | Number of items sold |
---|---|

Sunday | 10 |

Monday | 15 |

Tuesday | 20 |

Wednesday | 10 |

Thursday | 40 |

Friday | 45 |

Saturday | 30 |

**Vertical bar graph or bar chart**

Example

**Horizontal bar graph or bar chart**

**Interpretation of the graphs**

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

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.

Example

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 4: Number of items sold on saturday and sunday**

Name of item | Number of items sold on saturday | Number of items sold on sunday |
---|---|---|

Shirts | 10 | 20 |

Pants | 30 | 20 |

Socks | 40 | 30 |

Ties | 30 | 70 |

Belts | 20 | 60 |

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

**Double bar graph**

**Interpretation of double bar graph**

- Maximum sale is on sunday for ties.
- Minimum sale is on saturday for shirts.
- Sale of shirts on sunday is more than on saturday.
- Sale of pants on saturday is more than on sunday.
- Sale of socks on saturday is more than on sunday.
- Sale of ties on sunday is more than on saturday.
- Sale of belts on sunday is more than on saturday.
- Sale of shirts, pants and belts are sold equally.
- On sunday shirts and pants are sold equally.

Pie graph is also a pictorial representation of numerical data, represented by sectors of
circle.

Pie graph consists of a circle. 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.

A pie graph is used to compare parts of a whole and the circle represents the whole. Some
steps need to be followed to represent the data into a pie graph.

- From the given data, find the sum of all given quantities.
- Divide the each given quantity by sum obtained in step 1 and multiply it by 360
^{0}to get the value of a sector angle or central angle.

Central angle = $\frac{\mathrm{value\; of\; given\; quantity}}{\mathrm{sum\; of\; all\; given\; quantities}}$ × 360 - Draw a circle of any radius.
- Construct the various sectors corresponding to its central angle in clockwise direction.
- 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.

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

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

Example

**Table 5: Expenditure of different items in a month**

Items of expenditure | Amount spent | Central angle |
---|---|---|

Food | 300 | $\frac{300}{1200}$ × 360 = 90° |

Rent | 400 | $\frac{400}{1200}$ × 360 = 120° |

Clothing | 150 | $\frac{150}{1200}$ = 45° |

Education | 250 | $\frac{250}{1200}$ = 75° |

Miscellaneous | 100 | $\frac{100}{1200}$ = 30° |

**Steps to draw pie graph**

Draw a circle of any radius.

Draw its radius.

Construct a sector of central angle of 90^{0} starting from the radius drawn in the above
step in clockwise or anticlockwise direction.

Draw other sectors of central angle 120^{0}, 45^{0}, 75^{0} and 30^{0}.

Shade all six sectors by different colors and label them.

**Pie chart**

**Interpretation of pie chart**

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

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.

Example

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

**Table 6: January temperature on different days**

Date | Maximum temperature |
---|---|

1 | 14° |

2 | 10° |

3 | 8° |

4 | 6° |

5 | 10° |

6 | 12° |

To draw a line chart, we take two axes x-axis and y-axis.

On the x-axis, we represent dates of month and on the y-axis we represent temperature.

We plot the ordered points (1, 14), (2, 10),(3, 8),(4, 6),(5, 10) and (6, 12) as points.

Then we join these points by line segment.

**Interpretation of line graph**

- The minimum temperature was recorded on December 4.
- On December 2 and December 5, the temperature was same as 10
^{0}C