## Key Concepts

- Making and Interpreting a Table
- Collect, Organise and Interpret Data in Order
- Create a Table from Data in a Tally Chart and a Bar Graph

- Using a Table
- Interpret Data in a Table Organised by Rows, Columns and Intersecting.

- Line Graph
- Read and Interpret Data from Line Graph

**Introduction: **

In this chapter, we will be learning about the following:

- Interpreting data in a tally chart and bar graph.
- Interpreting data in a picture graph.
- Collecting data and making a line graph.

**4.1: Making and Interpreting a Table**

**Definition of data interpretation:** Data interpretation is the process of making sense out of the collection of data that has been processed. This collection may be present in various forms like bar graphs, line charts and tabular forms.

**4.1.1: Collect, Organize and Interpret Data in Order.**

**Data handling:** Data handling is gathering and recording information and then presenting it in a way that can be understood easily and used by other people.

**Example:** Here is a list of the number of students who did not complete their homework throughout one month.

1, 1, 3, 3, 4, 3, 3, 5, 6, 1, 1, 1, 2, 2, 3

**Sol.:** Organize the data by putting it in numerical order.

1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 3, 3, 4, 5, 6

Then represent the data in a table.

Number of students who did not complete homework | Frequency |

1 | 5 |

2 | 2 |

3 | 5 |

4 | 1 |

5 | 1 |

6 | 1 |

**Frequency:** Frequency refers to the number of times an event or a value occurs.

**4.1.2: Creating a Table from Data in a Tally Chart and a Bar Graph.**

**Tally chart:** Tally marks help in counting the frequency of occurrence of something. It is used for record-keeping.

**Example:** The scores obtained in 20 throws of dice are:

5, 4, 3, 2, 1, 1, 2, 6, 4, 6, 6, 6, 3, 21, 4, 3, 2, 2, 4

**Sol.:** Frequency table of scores in 20 throws:

Scores | Tally marks | Frequency |

1 | III | 3 |

2 | -||||- | 5 |

3 | III | 3 |

4 | IIII | 4 |

5 | II | 2 |

6 | III | 3 |

**Total = 20**

**Bar graph:** A bar graph is a chart that plots data using rectangular bars or columns that represent the total amount of observations in the data for that category.

**Example:** The bar graph shows the favorite type of movie that people liked.

**Favorite type of movie:**

Show the table by using a bar graph.

**Sol.: **Favorite type of movie

Comedy | Action | Romance | Drama |

4 | 5 | 6 | 1 |

**4.2: Using a Table**

**4.2.1: Interpret Data in a Table ****Organized**** by Rows, Columns and Intersecting.**

**Data interpretation in a table:** In tables, data is given in rows and columns. In the tabular method, data is arranged in vertical and horizontal rows. It is the easiest way of representing data but not the easiest way of interpreting data.

**Example:** The table shows the number of mobile phones that were sold by the showroom from the year 2010 to 2014. Answer the below questions based on the information given in the table.

Years | A | B | Total |

2010 | 183 | 123 | 306 |

2011 | 178 | 272 | 450 |

2012 | 133 | 160 | 293 |

2013 | 260 | 106 | 366 |

2014 | 279 | 272 | 551 |

**Questions:**

1. In the year 2012, how many mobiles were sold?

**Sol.:** 2012 = 133 + 160 = 293 phones were sold.

2. In the year 2010, showroom ‘A’ has sold __ phones.

**Sol.:** 183.

3. What was the total phones sold together from 2010 to 2012?

**Sol.:** 306 + 450 + 293 = 1049

4. How many showrooms are there?

**Sol.:** Two.

5. Total number of mobile phones that were sold by ‘B’?

**Sol.:** 123 + 272 + 160 + 106 + 272 = 933

### 4.3: Line Graphs

#### 4.3.1: Reading and Interpreting Data from Line Graphs.

**Line graph:*** *A line graph is a type of chart used to show information that changes over time. We plot line graphs using several points connected by straight lines. It is also called a line chart. The line graphs comprise two axes known as the ‘x’-axis and ‘y’-axis.

- The horizontal axis is known as the x-axis.

- The vertical axis is known as the y-axis.

**Example:** The table shows Jack’s weight in kilograms for 5 months.

Jack’s Weight

Month | Jan | Feb | Mar | Apr | May |

Weight in kg | 49 | 54 | 61 | 69 | 73 |

The data from the table above has been represented in the graph below.

**Questions:**

1. What is the title of this graph?

**Sol.:** Jack’s weight.

2. What is the range of values on the horizontal scale?

**Sol.:** January to May.

3. What Is the range of values on the vertical scale?

**Sol.:** 0 to 80.

4. How many points are in the graph?

**Sol.:** 5.

5. What was the highest value recorded?

**Sol.:** 73 kg.

6. What was the lowest value recorded?

**Sol.:** 49 kg.

7. Did Jack’s weight increase or decrease over time?

**Sol.:** Increased.

### Exercise:

- The table shows the number of students who have traveled on bus and train.

Bus | Train | |

Girls | 7 | 14 |

Boys | 8 | 5 |

- How many more boys traveled on the bus than girls?
- How many girls traveled by bus and train?

- What is the total number of students who have traveled on the train?

- The graph shows the number of football goals scored by teams. Read the graph to answer questions.

Goals scored by teams

- Which team scored the highest number of goals?
- What is the difference between the number of goals scored by team C and E?

- How many times has team C scored more than Team D?

- The table shows the number of books borrowed from the school library. Read the table to answer the questions.

Number of borrowed books | |

Monday | 13 |

Tuesday | 5 |

Wednesday | 2 |

Thursday | 18 |

Friday | 25 |

- How many books were borrowed on Monday and Wednesday?
- On which day the number of books borrowed was 5 times more than Tuesday?

- What is the difference between the highest and the lowest number of borrowed books?

- On how many days were more than 15 books borrowed?

- On which day the number of books was 9 times more than Wednesday?

- The graph below shows the number of cars sold in five days. Study the graph and answer the questions.

Weekly Car Sales

- How many cars were sold in all days?
- How many cars were sold on Wednesday?

- Which day had the minimum sales of cars?

- How many more cars were sold on Tuesday than on Monday?

### Concept Map:

### What have we learned:

In this chapter, we learned:

- The understanding of data presented in tables and graphs.
- The data presented in tables and graphs is easier to understand and interpret.
- The understanding of tally charts.
- What table graphs and bar graphs are.